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.
+9466 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
from the quadratic formula:
\(w = {-56 \pm \sqrt{56^2-4(2)(-1920)} \over 2(2)} = \frac{-56\pm \sqrt{18496}}{4}=\frac{-56\pm 136}{4}=-14\pm 34\)
Since we are looking for the length of a line, the answer is positive.
w = -14 + 34 = 20
and
height = 20 + 28 = 48 inches
+9466 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
from the quadratic formula:
\(w = {-56 \pm \sqrt{56^2-4(2)(-1920)} \over 2(2)} = \frac{-56\pm \sqrt{18496}}{4}=\frac{-56\pm 136}{4}=-14\pm 34\)
Since we are looking for the length of a line, the answer is positive.
w = -14 + 34 = 20
and
height = 20 + 28 = 48 inches
