Respuesta :
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 [tex]48 in\times 168 in[/tex]
(a)To calculate the side length of the largest square piece, we need to find the Greatest Common Factor (GCF) of the dimensions as:
[tex]48 = 2\times 2\times 2\times 2\times 3[/tex]
[tex]168 = 2\times 2\times 2\times 3\times 7[/tex]
Therefore,
The GCF of the dimensions = [tex]48 = 2\times 2\times 2\times 3 = 24[/tex]
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 = [tex]\frac{Total\ Area}{Area\ of\ largest\ square}[/tex]
No. of pieces = [tex]\frac{48\times 168}{24\times 24}[/tex] = 14
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)
[tex]48=2\times 2\times 2\times 2\times 3[/tex]
[tex]168=2\times 2\times 2\times 3\times 7[/tex]
HCF(48,168)=[tex]2\times 2\times 2\times 3=24[/tex]
Hence, the largest side of square=24 inches.
b.We have to find number of pieces of square.
Area of rectangle=[tex]length \times breadth[/tex]
Area of rectangle=[tex]48\times 168=8064 in^2[/tex]
Area of square=[tex]side\times side[/tex]
Area of square=[tex]24\times 24=576 in^2[/tex]
Number of piece of square=[tex]\frac{8064}{576}=14[/tex]
Hence, the number of piece of square=14
