Answer:
The perimeter of the smaller square is 24 inches.
Step-by-step 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:
[tex]\frac{\text{Area of MNPQ}}{\text{Area of RSTU}}=\frac{16}{9}[/tex]
[tex]\frac{64}{x}=\frac{16}{9}[/tex]
Now solve for x.
[tex]x=4\times 9[/tex]
[tex]x=36[/tex]
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.
