# Chapter 1 - Section 1.1 - Angles, Degrees, and Special Triangles - 1.1 Problem Set: 64

Each shorter side = $6\sqrt 2$

#### Work Step by Step

In a 45°–45°–90° triangle,let's assume that each of the shorter side is 'x'. then as per Pythagorean theorem- $longest side^{2}$ = $x^{2} + x^{2}$ = 2$x^{2}$ Therefore longest side = $x\sqrt 2$ Given that longest side is $12$ Hence $x\sqrt 2$ = 12 Dividing both the sides by $\sqrt 2$ x = $\frac{12}{\sqrt 2}$ or x = $\frac{6\sqrt 2\sqrt 2}{\sqrt 2}$ = $6\sqrt 2$ Thus each shorter side = $6\sqrt 2$

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