Ratio of length to width with area

Question

The area of a rectangle is 250 in². The ratio of the length to the width is 5:2. Find the length and the width.

Answer 1

The area of a rectangle is 250 in². The ratio of the length to the width is 5:2. Find the length and the width.

A ratio of x : y means that there is an integer n such that the ratio of n*x : n*y is the same. This is why a ratio like nx : ny may be reduced (just like a fraction) to x : y.

The area of area of a rectangle is L*W. Let's find n such that the ratio 5n : 2n is the same as the ratio L : W.

A = L*W

250 = 5n*2n = 10n²

n² = 25

n = 5 [note: n=-5 does not make sense]

The rectangle is 25 inches x 10 inches.