Question

The diagonal of a rectangle is 13 inches. The length of the rectangle is 7 inches longer than its width. How do you find the length and width of the rectangle?

Answer 1

Let's call the width `x`. Then the length is `x+7`

Explanation:

The diagonal is the hypotenuse of a rectangular triangle.
So:
`d^2=l^2+w^2` or (filling in what we know)

`13^2=169=(x+7)^2+x^2=x^2+14x+49+x^2->`

`2x^2+14x-120=0->x^2+7x-60=0`

A simple quadratic equation resolving into:

`(x+12)(x-5)=0->x=-12orx=5`

Only the positive solution is useable so:

`w=5 and l=12`

Extra :
The (5,12,13) triangle is the second-simplest Pythagorean triangle (where all sides are whole numbers). The simplest is (3,4,5). Multiples likes (6,8,10) don't count.