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?

Question

asked Jun 21, 2018 97.0k views

2 Answers

DeFrenZ · Answer 1 · 2018-06-25T20:14:59+0000

Answer:

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.