Question

The lengths of corresponding sides of two squares are in the ratio of 3:1. If the area of the larger square exceeds the area of the smaller square by 63 in.², find the area of the smaller square

Answer 1

Answer:

The area of the smaller square is 7.875 square inches

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Remember that all the squares are similar

Let

z ----> the scale factor

x ---> the area of the larger square

y ---> the area of the smaller square

so

$z^2=\frac{x}{y}$

we have

$z=\frac{3}{1}=3$ ---> scale factor

substitute

$3^2=\frac{x}{y}$

$x=9y$ ----> equation A

That means---> the area of the larger square is 9 times greater than the area of the smaller square

The area of the larger square exceeds the area of the smaller square by 63 in.²

so

$x=y+63$ ----> equation B

Equate equation A and equation B

$9y=y+63$

solve for y

$9y-y=63\\8y=63\\y=7.875\ in^2$

therefore

The area of the smaller square is 7.875 square inches