Question

Squares MNPQ and RSTU are similar. The ratio of their areas is 16:9. If the larger square has a side length of 8 inches, what is the perimeter of the smaller square?

Answer 1

The perimeter of the smaller square will be 24 inches!

Answer 2

The perimeter of the smaller square is 24 inches.

Explanation:

Consider the provided information.

The larger square has a side length of 8 inches,

The area of square is: (side)²

The area of large square MNPQ is: (8)²= 64 inches²

Let the area of small square RSTU is x inches².

Squares MNPQ and RSTU are similar. The ratio of their areas is 16:9.

This can be written as:

`\frac{\text{Area of MNPQ}}{\text{Area of RSTU}}=(16)/(9)`

`(64)/(x)=(16)/(9)`

Now solve for x.

`x=4* 9`

`x=36`

Hence, the area of of small square RSTU is 36 inches².

The side of small square RSTU is:

36 = (side)²

6 = side

The perimeter of square is: 4(side)

The perimeter of the smaller square is:

Perimeter = 4×6=24 inches

Hence, the perimeter of the smaller square is 24 inches.