SOLUTION: The area of a rectangle is 21 cm square. If one side exceeds the other by 4 cm, Find the dimensions of the rectangle.
Algebra.Com
Question 1199532: The area of a rectangle is 21 cm square. If one side exceeds the other by 4 cm, Find the dimensions of the rectangle.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Answer: 3 cm by 7 cm rectangle
3*7 = 21
=======================================================================
Explanation:
Let's list the ways to factor 21 with positive values:
1*21 = 21
3*7 = 21
The gap from 3 to 7 is 4 units, because 7-3 = 4, so it's fairly clear that we have a 3 by 7 rectangle.
--------------------------------------------
Another approach using algebra.
x = width
x+4 = length which is four units larger than the width
area = length*width
area = (x+4)*x
area = x^2+4x
We'll set this equal to the stated area 21 square cm, and solve for x.
x^2+4x = 21
x^2+4x-21 = 0
From here you can factor like so
x^2+4x-21 = 0
(x-3)(x+7) = 0
x-3 = 0 or x+7 = 0
x = 3 or x = -7
Ignore x = -7 because it makes no sense to have a negative length or width.
If x = 3, then x+4 = 3+4 = 7
We arrive at 3*7 = 21 to confirm the answers.
Another way to solve x^2+4x-21 = 0 is to use the quadratic formula.
We have
a = 1
b = 4
c = -21
to get the following steps:
or
or
or
Then as mentioned earlier, we ignore the negative x value and have x = 3 lead to x+4 = 7.
RELATED QUESTIONS
the area of a rectangle is 21 cm square if one side exceeds the other by 4 cm find the... (answered by Alan3354)
The area of a rectangle is 21 cm2.If one side exceeds the other by 4 cm,what is the... (answered by Alan3354)
one side of a rectangle is 8 cm more than the other. If the diagonal of the rectangle is... (answered by poliphob3.14)
One side of the rectangle exceeds three times the other side by 2cm. Find the length of... (answered by ewatrrr)
one side of a rectangle is 7 cm more than the other. if the diagonal of the rectangle is... (answered by stanbon)
The perimeter of a square and a rectangle are equal. One side of the rectangle is 11 cm... (answered by jorel555)
A square has an area of 256 cm^2. If the same amount is removed from one dimension and... (answered by MathLover1)
One side of a rectangle is 4 feet longer than the other side. If the rectangle has an... (answered by jojo14344)
One side of a rectangle is 4 feet longer than the other side. If the rectangle has an... (answered by checkley75)