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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
