Question

A rectangle has side lengths in the ratio 2:3. The ratio of the rectangles's perimeter to its area is 5:9. What is the length of the longer leg of the rectangle?

Answer 1

let the width be 2x and the length be 3x

Area = 6x^2
perimeter = 10

10x/6x^2 = 5/9
30x^2 = 90x

divide by 30 and factor
x(x-3) = 0
x = 0 or x = 3, x=0 is not admissable (we have to have some sort of a width)

the width is 6 and the length is 9

check:
area = 54
perimeter = 30
what is 30/54 ??