Question

A rectangle's length is three times its width, and its perimeter is 210 inches longer than its width. Find the width and length.

a) Width = 35 in, Length = 105 in
b) Width = 45 in, Length = 135 in
c) Width = 30 in, Length = 90 in
d) Width = 42 in, Length = 126 in

Answer 1

The width of the rectangle is 30 inches and the length is 90 inches.

Step-by-step explanation:

Let's call the width of the rectangle 'w'. Since the length is three times the width, we can write the length as '3w'. The perimeter is 210 inches longer than the width, so we can write the equation: 2(w + 3w) = w + 210.

First, simplify the equation: 2(4w) = w + 210. Then, multiply: 8w = w + 210. Subtract 'w' from both sides: 7w = 210. Divide both sides by 7: w = 30.

So, the width of the rectangle is 30 inches, and the length is 3w = 3(30) = 90 inches. Therefore, the correct answer is option c) Width = 30 in, Length = 90 in.