Asquare 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.

 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

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.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.