Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 4 - Congruent Triangles - 4-5 Isosceles and Equilateral Triangles - Practice and Problem-Solving Exercises - Page 255: 28


$x = 6$

Work Step by Step

The perimeter of a triangle is the sum of the length of each of its sides. We are given expressions for the lengths of the legs and base of an isosceles triangle along with the value of its perimeter. If we add up the lengths of the legs and the base of the triangle, they should equal the perimeter. Let's set up this equation: $2(legs) + base$ = perimeter of the triangle Let's plug in what we know: $2(2x - 5) + x = 20$ Use the distributive property to get rid of the parentheses: $4x - 10 + x = 20$ Combine like terms: $5x - 10 = 20$ Add $10$ to both sides of the equation to isolate the $x$ term: $5x = 30$ Divide each side of the equation by $5$ to solve for $x$: $x = 6$
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