Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Lesson Check: 5

Answer

The student incorrectly substituted the given length of the hypotenuse (13) into the equation where the length of a leg should have been used. x=5

Work Step by Step

In the equation $a^2+b^2=c^2$, a and b are the lengths of the two legs and c is the length of the hypotenuse. $a^2+b^2=c^2\longrightarrow$ substitute the given values $12^2+x^2=13^3\longrightarrow$ compute the squares $144+x^2=169\longrightarrow$ subtract 144 from each side $144+x^2-144=169-144\longrightarrow$ subtract $x^2=25\longrightarrow$ find the square root of each side $\sqrt {x^2}=\sqrt {25}\longrightarrow$ simplify $x=5$
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