The width of a rectangle is 2 inches shorter than the length and the perimeter is 80. Set up an equation for the perimeter involving only L, the length.Find the width as well.
Perimeter = 2L + 2W = 2L + 2(L-2)
= 4L - 4 = 80
L = 21
W = L-2 = 19
Perimeter=2L+2W=2L+2(L-2)
= 4L-4 =80
L = 21
W = L-2 = 19
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To solve this problem, let's start by setting up an equation for the perimeter involving only the length of the rectangle.
The perimeter of a rectangle is the sum of all four sides. In this case, we know that the width is 2 inches shorter than the length.
So, if we let L represent the length of the rectangle, the width would be L - 2.
The formula for the perimeter of a rectangle is: P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Given that the perimeter is 80, we can substitute the values into the equation:
80 = 2L + 2(L - 2)
Expanding the equation:
80 = 2L + 2L - 4
Combining like terms:
80 = 4L - 4
Adding 4 to both sides of the equation:
80 + 4 = 4L
Simplifying:
84 = 4L
Dividing both sides of the equation by 4:
L = 21
Therefore, the length of the rectangle is 21 inches.
To find the width, substitute the value of L back into the equation:
W = L - 2
W = 21 - 2
W = 19
Therefore, the width of the rectangle is 19 inches.