A rectangle is drawn so the width is 6" longer than the height. If the rectangles diagonal measurement is 59", find the height give your answer rounded to one decimal place in inches

Answer 1

The diagonal of a rectangle is the hypotenuse of a right triangle whose altitude (height) is h and base (width) is h + 6.

So, by the pythagorean theorem h^2 + (h+ 6)^2 = 59^2.

This leads to 2h^2 + 12h -3445 = 0.

Solve by quadratic formula and get h = 38.6 inches.

Answer 2

We can use the Pythagorean theorem to set up an equation for the height h:

h² + (h + 6)² = 59² = 3481

2h² + 12h - 3445 = 0

When we use the quadratic formula to solve this, we have

h = -12±√(144+27560)/4,

and the one logical solution for this is

h ~ 38.6"

We can check this with by plugging it into the first equation:

38.6² + 44.6² = 3479.1 < 3481

38.7² + 44.7² = 3495.8 > 3481