A square quilt for a child's bed has a border made up of 32 pieces with an area of x each, and 4 small squares with an area of 1 square inch each. The main part of the quilt is made of 64 squares with an area of x squared each.
If the quilt is 4 ft by 4 ft, what are the dimensions of the inside squares?
Total area = sum areas
16 = 32x + 4 + 64x^2
solve for x.
To find the dimensions of the inside squares in the quilt, we need to solve the equation:
Total area = sum of areas
Given that the quilt is 4 ft by 4 ft, the total area is 4 ft * 4 ft = 16 square feet.
Now, let's break down the areas of different components of the quilt:
1. The border is made up of 32 pieces with an area of x each. So, the total area of the border is 32x square feet.
2. There are 4 small squares with an area of 1 square inch each. Since one square foot is equal to 144 square inches, the total area of the small squares is (4 * 1) / 144 = 4 / 144 square feet.
3. The main part of the quilt is made of 64 squares with an area of x squared each. So, the total area of the main part is 64 * x^2 square feet.
Now, we can set up the equation:
16 = 32x + (4 / 144) + 64x^2
To solve for x, we can simplify the equation and rearrange it:
16 = 32x + (1 / 36) + 64x^2
64x^2 + 32x - (16 - (1 / 36)) = 0
Now, we can solve this quadratic equation for x using any suitable method, such as factoring, completing the square, or using the quadratic formula. Once we find the values of x, we can use them to calculate the dimensions of the inside squares.