Question

A square mirror has sides measuring 2 ft less than the sides of a square painting. If the difference between their areas is 32 ft. Find the lengths of the sides of the mirror and the painting.

Answer 1

Answer:  The side lengths of mirror and painting are 7 ft and 9 ft respectively.

Step-by-step explanation:  Given that a square mirror has sides measuring 2 ft less than the sides of a square painting and the difference between their areas is 32 ft.

We are to find the lengths of the sides of the mirror and the painting.

Let x ft represents the length of the side of mirror. Then, the side length of square painting is (x+2) ft.

According to the given information, we have

$\textup{area of painting}-\textup{area of mirror}=32\\\\\Rightarrow (x+2)^2-x^2=32\\\\\Rightarrow x^2+4x+4-x^2=32\\\\\Rightarrow 4x=28\\\\\Rightarrow x=\dfrac{28}{4}\\\\\Rightarrow x=7.$

Therefore, the side length of mirror is 7 ft and the side length of painting is (7+2) = 9 ft.

Thus, the side lengths of mirror and painting are 7 ft and 9 ft respectively.