Question

Shelly and Mickelle are making a quilt. They have a piece of fabric that measures 48 inches by 168 inches.

Answer 1

Answer:

(a) The largest square side is 24 inches

(b) No. of pieces are 14

Step-by-step explanation:

As per the question:

The dimensions of the fabric are $48 in\times 168 in$

(a)To calculate the side length of the largest square piece, we need to find the Greatest Common Factor (GCF) of the dimensions as:

$48 = 2\times 2\times 2\times 2\times 3$

$168 = 2\times 2\times 2\times 3\times 7$

Therefore,

The GCF of the dimensions = $48 = 2\times 2\times 2\times 3 = 24$

Therefore, the largest side of  a square that can be cut from the fabric is 24 inches.

(b) The no. of pieces of 24 inches that can be cut from the fabric can be given as:

No. of pieces = $\frac{Total\ Area}{Area\ of\ largest\ square}$

No. of pieces = $\frac{48\times 168}{24\times 24}$ =  14

Answer 2

Answer:

a.24 inches

b.14

Step-by-step explanation:

We are given that

Length of piece of fabric=48 inches

Width of piece of fabric=168 inches

a.We have to find the side length of the largest square piece.

To find HCF (48,168)

$48=2\times 2\times 2\times 2\times 3$

$168=2\times 2\times 2\times 3\times 7$

HCF(48,168)=$2\times 2\times 2\times 3=24$

Hence, the largest side of square=24 inches.

b.We have to find number of pieces of square.

Area of rectangle=$length \times breadth$

Area of rectangle=$48\times 168=8064 in^2$

Area of square=$side\times side$

Area of square=$24\times 24=576 in^2$

Number of piece of square=$\frac{8064}{576}=14$

Hence, the number of piece of square=14