Question 1182601
A rectangle is drawn so the width is 5 inches longer than the height. If the rectangle's diagonal measurement is 28 inches, find the height.
<pre>Let height be H
Then width = H + 5
Using the Pythagorean formula, we get: H<sup>2</sup> + (H + 5)<sup>2</sup> = 28<sup>2</sup>
                                       H<sup>2</sup> + H<sup>2</sup> + 10H + 25 = 784
                                       2H<sup>2</sup> + 10H + 25 - 784 = 0
                                       2H<sup>2</sup> + 10H - 759 = 0
To get the height, solve the above equation for H, using the Quadratic Equation formula, or by Completing the Square.
Then, DISCARD the negative value for H since a measurement CANNOT be < 0.