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?

1 Answer
Oct 15, 2015

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

Explanation:

The diagonal is the hypotenuse of a rectangular triangle.
So:
d^2=l^2+w^2d2=l2+w2 or (filling in what we know)

13^2=169=(x+7)^2+x^2=x^2+14x+49+x^2->132=169=(x+7)2+x2=x2+14x+49+x2

2x^2+14x-120=0->x^2+7x-60=02x2+14x120=0x2+7x60=0

A simple quadratic equation resolving into:

(x+12)(x-5)=0->x=-12orx=5(x+12)(x5)=0x=12orx=5

Only the positive solution is useable so:

w=5 and l=12w=5andl=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.