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Question 1189165: Dear Colleagues
I have the following question to find a solution to:
The length of a rectangle exceeds its breadth by 4 centimetres. If the length were halved and the breadth increased by 5 centimetres, the area would be decreased by 35 square centimetres. Find the length of the rectangle.
I do not know if I can draw in this website, but whilst trying to find the solutions, I drew 2 rectangles: the one on the left had the dimensions (x)(x+4) for width and length respectively, the one on the right had dimensions ((x+4)/2)(x+5) for length and width respectively.
The question then reads - for me - [((x+4)/2)(x+5)] - 35 = x(x+4)
Multiplying the left hand by 2 to clear the fraction, we get
[(x+4)(2x+10)]-35 = x(x+4)
and after multiplying out we get
[2x^2+10x+8x+40]-35 = x^2+4x
Collecting like terms gives us
2x^2+18x+5 = x^2+4x
which simplifies to
x^2+14x+5=0
We cannot factorise, so using the quadratic formula we get
a = 1, b= 14, c = 5
and putting all of this into the formula we get
x = (-b+/- sqrt of b^2-4ac)/2
which gives
x = (-14 +/- sqrt (14)^2-(4)(1)(5))/2
which gives us, finally, x = (-14 +/-13.23)/2
I am assuming that we need a real number for the length of the side of the rectangle, so do not wish to get into imaginary numbers...
Where have I gone wrong?
Click here to see answer by MathTherapy(10552)

Question 1189333: The length of a rectangle is 1 cm less than three times the width if the perimeter is 54 cm find the dimensions of the rectangle use the formula to find the dimension P=2l+2w
Click here to see answer by Alan3354(69443)

Question 1189472: A solid rectangular prism with sides of 6 m by 9 m by 17 m is painted orange and then cut into 1 m^3 cubes. How many cubes are orange on fewer than 2 sides?
Click here to see answer by ikleyn(52780)

Question 1190318: PQRS is a rectangle and T is a point on line segment PQ with ∠RTS = 90°. If RT = 80 and PQ = 89, what is the area of rectangle PQRS?
Click here to see answer by ikleyn(52780)

Question 1190435: The width of a rectangle is 25.7 feet less than four times its length, and the perimeter is 29.6 feet. Find the length and the width of the rectangle
Click here to see answer by josgarithmetic(39617)

Question 1191362: Calculate the average rate of change of area with respect to width on the graph between the points where width=2 and width=6

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Question 1191364: Use the graph to determine a possible area for a width of 5,5cm indicate where the answer could be read off with the letter A
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Question 1191716: Draw 11 rectangles with a perimeter of 24 cm. For the width use natural numbers indicate the length the width and the area on the sketch of each rectangle
Click here to see answer by greenestamps(13200)

Question 1192099: Two similar rectangular prisms have an edge of the proportion of 3:5. If the smaller prism has a surface area of 69 m.squared, Find the surface area of the bigger prism. If the bigger prism has a volume of 500 m.squared, find the volume of the smaller prism.
Click here to see answer by ikleyn(52780)

Question 1192108: Two similar rectangular prisms have an edge of the proportion of 3:5. If the smaller prism has a surface area of 69 m.squared, Find the surface area of the bigger prism. If the bigger prism has a volume of 500 cubic meters, find the volume of the smaller prism.
Click here to see answer by ikleyn(52780)

Question 1192143: Consider the domain, classify this relationship as either discrete or continuous. Give a reason for your answer
Click here to see answer by greenestamps(13200)

Question 1193033: The length of a driveway is 32 feet and the width is 16 feet. How many bricks would it take to fill the driveway? *One brick is 7 inches in length and 3 1/2 inches in width.*
Click here to see answer by Alan3354(69443)

Question 1193299: what is the step by step solution to w(2w+1)=15 and how do I discover what the width is
Click here to see answer by MathLover1(20849)

Question 1193299: what is the step by step solution to w(2w+1)=15 and how do I discover what the width is
Click here to see answer by josgarithmetic(39617)

Question 1193299: what is the step by step solution to w(2w+1)=15 and how do I discover what the width is
Click here to see answer by ikleyn(52780)

Question 1193300: the rectangles area is fours square units. the height plus twice the width is 6 units. step by step please
Click here to see answer by Theo(13342)

Question 1193793: The park across the street is to be treated to control a new algae that is growing on
top of the grass. After 𝑡 days of treatment the concentration of algae per square
metre is given by 𝐴(𝑡) = 25𝑡
2 − 300𝑡 + 1200. Determine the lowest concentration
of algae in the first week after the treatment. Prove it is the lowest. [5 marks]

Click here to see answer by josgarithmetic(39617)

Question 1193792: The park across the street is to be treated to control a new algae that is growing on
top of the grass. After 𝑡 days of treatment the concentration of algae per square
metre is given by 𝐴(𝑡) = 25𝑡
2 − 300𝑡 + 1200. Determine the lowest concentration
of algae in the first week after the treatment. Prove it is the lowest. [5 marks]

Click here to see answer by josgarithmetic(39617)

Question 1194090: A rectangle 9cm is equal in area to a square which has a perimeter of 24 cm. Find the width of the rectangle

Click here to see answer by Alan3354(69443)

Question 1194117: Find the value of x as it relates to the rectangle.
Area: 60 cm^2
Length:x
Width:x+4
Click here to see answer by ikleyn(52780)

Question 1194924: The curve y=x^2-3x-4 cuts the x-axis at A and B. The tangents to the curve at A and B meet at T, and the normals to the curve at A and B meet at N. Find the area of the quadrilateral ATBN.
Click here to see answer by ikleyn(52780)

Question 1195181: I want to take a number and form a square or rectangle.
For example:
Triangluar Numbers
input = 28 --> 7 columns * 4 rows
input=45 --> 9 columns * 5 rows
input = 66 --> 11 columns * 6 rows
Non Triangular Numbers
input = 69 --> 7 columns * 9 rows (get as close to a square as possible)
TIA
Millamber
Click here to see answer by josgarithmetic(39617)

Question 1196546: The length of a rectangle is 3 units shorter than twice the width, x.
Which expression represents the perimeter of the rectangle?
Hint: sketch a picture of the rectangle and label the sides.

Responses
4x +6
4x +6,
2x + 3
2x + 3
6x - 6
6x - 6,
4x - 3
4x - 3,
Skip to navigation

Click here to see answer by ikleyn(52780)

Question 1196598: The perimeter of a Jamaican flag is 60 inches. The length is twice its width. Find the dimensions of the flag.
Click here to see answer by MathLover1(20849)

Question 1196603: A rectangular field is three times as long as it is wide. If the perimeter of the field is 640 feet, what is the length and width of the field?
Click here to see answer by ewatrrr(24785)

Question 1196616: The length of a rectangle is twice it's width. If the width is reduced by 1cm and the length is reduced by 2cm, the area will be 15cm². The dimensions of the original rectangle.
Click here to see answer by ewatrrr(24785)

Question 1196633: a notebook has an area of 150m² and a perimeter of 50cm. what are the dimensions of the notebook
Click here to see answer by Theo(13342)

Question 1196633: a notebook has an area of 150m² and a perimeter of 50cm. what are the dimensions of the notebook
Click here to see answer by greenestamps(13200)

Question 1196634: the area of rectangular garden should be at least 250 square meters. If its length is 5 meters more than twice its width, find the range of the possible values for the lot's length and width.
Click here to see answer by greenestamps(13200)

Question 1196668: You work for a tile manufacturing company. The company has overstocked a certain set of tiles. There are three different tiles in this particular
set. One is a large square tile, the second is a small square tile and the third
is a rectangle. The length of the rectangle is the same length as one side of
the large square. The width of the rectangle is the same size as one side of
the small square. This happens to work out to be good news. A set of these tiles can be arranged into rectangular configurations to create nice tile patterns.
Find all the rectangular configurations that can be made using 6 large
squares and 4 small squares along with only 2 rectangles.
How many rectangles are needed to make a rectangular configuration? Answer: 2
Explain how you know.??
Illustrate all the different configurations that can be created.???
Explain how you know that you have found all possible rectangular
configurations.???
Click here to see answer by ikleyn(52780)

Question 1196695: An open-topped box is constructed froma square piece of cardboard by removing a square of size 5 inches from each corner and turning up the edges.
If the box is to hold 9,680 in3, how big should the originial piece of cardboard be?
Click here to see answer by MathLover1(20849)

Question 1196860: Find the perimeter and area of a basketball court whose dimensions are 94ft by 50 ft
Click here to see answer by ikleyn(52780)

Question 1197198: Let ABCD be a rectangle and M a point inside it.

Prove that (MA)^2 + (MC)^2 = (MB)^2 + (MD)^2
Click here to see answer by math_tutor2020(3816)

Question 1197198: Let ABCD be a rectangle and M a point inside it.

Prove that (MA)^2 + (MC)^2 = (MB)^2 + (MD)^2
Click here to see answer by ikleyn(52780)

Question 1197300: Suppose the area of the swimming pool is doubled, would its length and width also doubled? Justify your answer. The length is 35 and the width is 16
Click here to see answer by math_helper(2461)

Question 1198015: The width of a rectangle is 18 centimeters more than the length. The perimeter is 44 centimeters. Find the length and width.
Click here to see answer by Alan3354(69443)

Question 1198015: The width of a rectangle is 18 centimeters more than the length. The perimeter is 44 centimeters. Find the length and width.
Click here to see answer by MathTherapy(10552)

Question 1198015: The width of a rectangle is 18 centimeters more than the length. The perimeter is 44 centimeters. Find the length and width.
Click here to see answer by josgarithmetic(39617)

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