You are making a square quilt with the design shown below. Find the side length x of the inner square that would make its area equal to 30% of the total area of the quilt. Round to the nearest tenth of a foot.
A large red outer square with a proportionately smaller yellow inner square is shown. Over the squares is a superimposed 5 by 5 grid with a size equal to the red square and the width in the outer square is measured 6 ft.
To find the side length x of the inner square that would make its area equal to 30% of the total area of the quilt, we first need to find the area of the outer square.
The area of the outer square is equal to the width squared, which is 6 ft * 6 ft = 36 sq ft.
Since the inner square is proportionately smaller, the area of the inner square would be 30% of the total area of the quilt, which is 0.3 * 36 sq ft = 10.8 sq ft.
To find the side length x of the inner square, we need to find the square root of its area.
x^2 = 10.8
x = √10.8
x ≈ 3.3 ft
Therefore, the side length x of the inner square that would make its area equal to 30% of the total area of the quilt is approximately 3.3 feet.