+0

# helpppp

0
138
1

A rectangle is drawn so the width is 28 inches longer than the height. If the rectangle's diagonal measurement is 52 inches, find the height.

Guest Apr 20, 2017

#1
+5541
+4

width = w

height = w + 28

from the Pythagorean theorem:

w2 + (w + 28)2 = 522

w2 + (w + 28)(w + 28) = 2704

w2 + w2 + 28w + 28w + 784 = 2704

2w2 + 56w - 1920 = 0

$$w = {-56 \pm \sqrt{56^2-4(2)(-1920)} \over 2(2)} = \frac{-56\pm \sqrt{18496}}{4}=\frac{-56\pm 136}{4}=-14\pm 34$$

Since we are looking for the length of a line, the answer is positive.

w = -14 + 34 = 20

and

height = 20 + 28 = 48 inches

hectictar  Apr 20, 2017
Sort:

#1
+5541
+4

width = w

height = w + 28

from the Pythagorean theorem:

w2 + (w + 28)2 = 522

w2 + (w + 28)(w + 28) = 2704

w2 + w2 + 28w + 28w + 784 = 2704

2w2 + 56w - 1920 = 0

$$w = {-56 \pm \sqrt{56^2-4(2)(-1920)} \over 2(2)} = \frac{-56\pm \sqrt{18496}}{4}=\frac{-56\pm 136}{4}=-14\pm 34$$

Since we are looking for the length of a line, the answer is positive.

w = -14 + 34 = 20

and

height = 20 + 28 = 48 inches

hectictar  Apr 20, 2017

### 14 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details