math
Suppose that the width of a rectangle is 5 inches shorter than the length and that the perimeter of the rectangle is 50 inches. The formula for the perimeter of a rectangle is P=2L+2W.
a) Set up an equation for the perimeter involving only L, the length of the rectangle.
B) Solve this equation algebraically to find the length of the rectangle. Find the width as well.
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Answers
A) P = 2L + 2(L - 5) B) Since the perimeter of the rectangle is 50 inches, P = 50. This can be substituted into the equation from part (A): 50 = 2L + 2(L - 5) 50 = 2L + 2L - 10 50 = 4L - 10 60 = 4L L = 15 The width of the rectangle W can be found by substituting L into the original equation for perimeter: P = 2L + 2W 50 = 2(15) + 2W 50 = 30 + 2W 20 = 2W W = 10 Therefore, the length of the rectangle is 15 inches and the width is 10 inches.
