Question

Two squares are drawn. the smaller square has an area of 256 square meters. the areas of the two squares have a ratio of 4:9.what is the side length s of the larger square.

Answer 1

side length of larger square = 24 meters

Explanation:

the smaller square has an area of 256 square meters. the areas of the two squares have a ratio of 4:9

Area of smaller square to larger square ratio is 4:9

Let 'area' be the area of larger square

Lets make a proportion using the given ratio and area of smaller square

`(4)/(9) =(256)/(area)`

cross multiply it

4 area = 256 times 9

Divide both sides by 4

`area= 576`

Area of larger square = 576 square meters

Are of square is (side )^2

`side^2= 576`

Take square root on both sides

side = 24

side length of larger square = 24 meters

Answer 2

A scale factor is the ratio of two similar geometric figures of their corresponding sides. The scale factor is calculated by locating the corresponding sides on each figure. We do as follows:

256/x = 4/9
x = 576 m^2

side length = 24 m

Hope this answers the question. Have a nice day.