Elementary Algebra

Published by Cengage Learning

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.5 - Factoring, Solving Equations, and Problem Solving - Problem Set 6.5 - Page 270: 95

Answer

The side is 17 inches long, and the altitude to that side is 6 in.

Work Step by Step

We know the following equation: $A = .5bh$ Since $b = 3h -1$, we obtain: $51 = .5(3h-1)(h) \\ 102 = 3h^2 -h \\ 3h^2 -h -102 = 0 \\ (h-6)(3h+17)$ Ignoring negative solutions, we find: $h = 6 \\ b = 3h -1 = 3(6) -1 =17$

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