Question

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

a. All pieces of fabric must be square with none left over. What is the side length of the largest square pieces into which Shelly and Mickelle can cut the fabric?
b. How many pieces of this size can Shelly and Mickelle cut?

Answer 1

a.24 inches

b.14

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* 2* 2* 2* 3`

`168=2* 2* 2* 3* 7`

HCF(48,168)=
`2* 2* 2* 3=24`

Hence, the largest side of square=24 inches.

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

Area of rectangle=
`length * breadth`

Area of rectangle=
`48* 168=8064 in^2`

Area of square=
`side* side`

Area of square=
`24* 24=576 in^2`

Number of piece of square=
`(8064)/(576)=14`

Hence, the number of piece of square=14

Answer 2

(a) The largest square side is 24 inches

(b) No. of pieces are 14

Explanation:

As per the question:

The dimensions of the fabric are
`48 in* 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* 2* 2* 2* 3`

`168 = 2* 2* 2* 3* 7`

Therefore,

The GCF of the dimensions =
`48 = 2* 2* 2* 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 =
`(Total\ Area)/(Area\ of\ largest\ square)`

No. of pieces =
`(48* 168)/(24* 24)` = 14