SOLUTION: a sqaure mirror has sides measuring 2 ft less than the sides of a square painting. if the difference between their areas is 32 ft^2, find the lengths of the sides of the mirror and

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Question 613649: a sqaure mirror has sides measuring 2 ft less than the sides of a square painting. if the difference between their areas is 32 ft^2, find the lengths of the sides of the mirror and the painting. the area of theb painting (-32)= the area of the mirror
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
x = length of one side of the mirror.
x+2 = length of one side of the painting.
area of the mirror is equal to x^2
area of the painting is equal to (x+2)^2 which is equal to x^2 + 4x + 4
difference between their areas is 32 square feet.
you get:
x^2 + 4x + 4 - x^2 = 32
simplify to get:
4x + 4 = 32
solve for x to get:
x = 7
length of one side of the mirror is equal to 7.
length of one side of the painting is equal to 9.
7^2 = 49
9^2 = 81
81 - 49 = 32
length of the side of the mirror is 7 feet.
length of the side of the painting is 9 feet.