Suppose the width of a rectangle is 5 inches shorter than the length and that the perimeter of the rectangle is 80 inches. The formula for the perimeter of a rectangle is P=2L + 2W. Set up an equation for the perimeter involving only the L the length of the rectancle.
And solve this linear equation algebracially to find the length of the rectangle and find the length as well
W+5=L-5
P=2W+2L=80
2(L-5)+2L=80
you finish it.
To set up an equation for the perimeter involving only the length (L) of the rectangle, we can use the given information.
Let's assume that the length of the rectangle is L inches. According to the problem, the width of the rectangle is 5 inches shorter than the length, so the width would be (L - 5) inches.
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.
Using the values we determined, we can substitute them into the perimeter formula:
P = 2L + 2(L - 5)
The problem also states that the perimeter of the rectangle is 80 inches, so we can substitute P = 80 into the equation:
80 = 2L + 2(L - 5)
To solve this linear equation algebraically, we can simplify and solve it step by step:
80 = 2L + 2L - 10
80 = 4L - 10
90 = 4L
L = 90/4
L = 22.5
Therefore, the length of the rectangle is 22.5 inches.