Answer:
The width is 16 inches while the length is 24 inches.
Step-by-step explanation:
We are given that the length (L) is 8 more than it's width (W).
The equation for this is: L=8+W.
We are given the perimeter is 80.
The equation for this is 2L+2W=80.
Each term here is even so I'm going to divide both sides by 2: L+W=40.
My system to solve is:
L=8+W
L+W=40
I'm going to plug the first equation into the second giving me:
(8+W)+W=40
Drop the (), don't really need:
8+W+W=40
Combine like terms:
8+2W=40
Subtract 8 on both sides:
2W=32
Divide both sides by 2:
W=32/2
Simplify:
W=16
So if W=16 and L=8+W then L=8+16=24.
The width is 16 inches while the length is 24 inches.
Perimeter is the sum of the length of the sides used to make the given figure. The length and the width of the rectangle are 24 inches and 16 inches, respectively.
Perimeter is the sum of the length of the sides used to make the given figure.
Let the width of the rectangle be represented by x.
Given that the length of a rectangle exceeds its width by 8 inches. Therefore, the length and the width of a rectangle can be written as,
Width = x inches
Length = x inches + 8 inches
Now, as it is given that the perimeter of the rectangle is 80 inches. Therefore, the perimeter of the given rectangle can be written as,
Perimeter of rectangle = 2(Length + Width)
80 inches = 2[(x+8) + x]
80 = 2(x + 8 + x)
80 = 2(2x + 8)
80/2 = 2x + 8
40 = 2x + 8
40 - 8 = 2x
32 = 2x
x = 32/2
x = 16 inches
Further, the length and the width of the rectangle can be written as,
Width = x = 16 inches
Length = x + 8 = 16 + 8 = 24 inches
Hence, the length and the width of the rectangle are 24 inches and 16 inches, respectively.
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