Question

Quilting (stitching together of layers of fabric) dates back to ancient Egypt, and the oldest quilt discovered is from about 5500 years ago. Today, many bedspread quilts consist of small squares sewn together. If you wanted to create a quilt for your bed measuring 42 inches by 78 inches, with squares of quilted fabric, what are the dimensions of the largest squares you could use? How many squares would there be?

Answer 1

The largest squares that can be used for a bedspread quilt measuring 42 inches by 78 inches are 6 inches by 6 inches. A total of 91 squares are needed to complete the quilt.

Step-by-step explanation:

To create a quilt for a bed measuring 42 inches by 78 inches using squares of quilted fabric, the largest square size that can be used is determined by the greatest common divisor (GCD) of the length and width of the quilt. The GCD of 42 and 78 is 6 inches, which is the largest dimension for a square that can evenly fit both the length and width of the quilt. Therefore, the dimensions of the largest squares that could be used are 6 inches by 6 inches. To calculate the number of squares needed, we divide each dimension of the quilt by the dimension of the square: 42 inches / 6 inches = 7 squares for the width and 78 inches / 6 inches = 13 squares for the length. Multiplying the number of squares in both the width and length will give us the total number of squares needed, which is 7 * 13 = 91 squares.