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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
+3375
+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
+3375
+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

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