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
MeneerNask
Oct 15, 2015

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.

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