# Chapter 1 - Section 1.1 - Angles, Degrees, and Special Triangles - 1.1 Problem Set: 42

x = 4

#### Work Step by Step

We will use given data about triangle ABC and Pythagoras Theorem to solve for 'x'- We know that - $c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem) $5^{2} =(x)^{2} + (x-1)^{2}$ Therefore - $25 = x^{2} + (x^{2} - 2x +1)$ $25 = 2x^{2} - 2 x + 1$ $2x^{2} - 2 x - 24$ = 0 $x^{2} - x - 12$ = 0 $x^{2} + 3 x -4x - 12$ = 0 $x (x+3) -4(x+3)$ = 0 $(x+3) (x-4)$ = 0 Therefore Either x = 4 or -3 As x is a length, it can not be negative, Therefore x = 4

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