Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 241: 19

Answer

20 ft

Work Step by Step

The length of the bridge is 104 ft, so each half of the bridge is 52 ft. The space between the endpoints of the bridge remains the same at 104 ft, with a gap in the middle of 8 ft. Dividing this per side, that would mean that half the raised bridge would be over (104 - 8) $\div$ 2 ft, or 48 ft. 52 ft will form the hypotenuse, with 48 ft and b ft forming the legs of the right triangle. We solve for x to find the height the bridge is raised. x$^{2}$ + 48$^{2}$ = 52$^{2}$ Subtract 48$^{2}$ from each side x$^{2}$ = 52$^{2}$ - 48$^{2}$ x$^{2}$ = 2704 - 2304 x$^{2}$ = 400 x = 20
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