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Question 152516This question is from textbook elementary and intermediate algebra concepts and applications
: Can somebody please help me im stuck
. Solve the following problems involving applications of polynomials.
a. A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of the photo?
b. A rectangular parking lot is 100 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500 ft diagonally.
c. Three consecutive odd integers are such that the square of the third is 264 more than the square of the second. Find the three integers.
This question is from textbook elementary and intermediate algebra concepts and applications
Answer by mangopeeler07(462)   (Show Source):
You can put this solution on YOUR website! A. A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of the photo?
Dimensions of the photo: w and w+3
Dimensions of photo plus the border: w+2 and w+3+2
Area of photo plus border: (w+2)(w+3+2)=108
(w+2)(w+3+2)=108
Simplify the parentheses
(w+2)(w+5)=108
FOIL
w^2+7w+10=108
Subtract 10 from both sides
w^2+7w=98
Subtract 98 from both sides
w^2+7w-98=0
Factor
(w+14)(w-7)=0
Solve for w
w=-14 or 7
Width is positive, so w=7
Dimensions of the photo: w and w+3
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Answer:
Dimensions of the photo: 7in and 10in
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B. A rectangular parking lot is 100 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500 ft diagonally.
Length=w+100
Width=w
Diagonal=500
Half of the rectangle= a right triangle with sides w+100, w, and 500 as the hypotenuse
Pythagorean theorem:
w^2+(w+100)^2=500^2
Simplify
w^2+w^2+200w+10000=250000
Combine like terms
2w^2+200w+10000=250000
Subtract 250000 from both sides
2w^2+200w-240000=0
Factor
2(w^2+100w-120000)=0
Factor again
2(w+400)(w-300)=0
Solve for w
w=-400 or 300
Width is positive, so w=300
Length=w+100
Width=w
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Answer:
Length=400ft
Width=300ft
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C. Three consecutive odd integers are such that the square of the third is 264 more than the square of the second. Find the three integers.
consecutive odd integers= x, x+2, x+4
(x+4)^2=(x+2)^2+264
Simplify
x^2+8x+16=x^2+4x+4+264
Combine like terms on each side
x^2+8x+16=x^2+4x+268
Subtract 4x from both sides
x^2+4x+16=x^2+268
Subtract 268 from both sides
x^2+4x-252=x^2
Subtract x^2 from both sides
4x-252=0
Add 252 to both sides
4x=252
Divide both sides by 4
x=63
consecutive odd integers= x, x+2, x+4
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Answer: 63, 65, and 67
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