Question

The design of a square rug for your living room is shown. You want the area of the inner square to be 25% of the total area of the rug. Find the side length x of the inner square.

One side of the rug is 6 ft

Answer 1

if the square rug has a side length of 6, we can say that the area of the rug is 36 ft²
since the inner square has an area 25% of the rug's area, you multiply 36 by 0.25 to get 9 ft²
since we know that the area of the inner square is 9 ft², we can find the length of the inner square since x²=9 ft².
x=3 ft

Answer 2

The side length of the inner square is 3 feet.

Let's denote the side length of the inner square as 'x' feet.

Since the area of the inner square is 25% of the total area of the rug, we can express this mathematically as:

x² = 0.25 * (6²), where '6²' represents the total area of the rug (6 feet x 6 feet).

Simplifying the equation:

x² = 0.25 * 36

x² = 9

Taking the square root of both sides:

x = √9

x = 3

Therefore, the side length of the inner square is 3 feet.