Algebra 1

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

Chapter 10 - Radical Expressions and Equations - Mid-Chapter Quiz: 20

Answer

$2w\sqrt{34}$ yd

Work Step by Step

The diagonal forms a right triangle. Use the Pythagorean Theorem to find the length from corner to corner. $a^2+b^2=c^2\longrightarrow$ substitute the given values $(6w)^2+(10w)^2=c^2\longrightarrow$ simplify $36w^2+100w^2=c^2\longrightarrow$ add $136w^2=c^2\longrightarrow$ find the square root of each side $\sqrt{136w^2}=\sqrt{c^2}\longrightarrow$ factor out the perfect square $\sqrt{4w^2\times34}=c\longrightarrow$ multiplication property of square roots $\sqrt{4w^2}\times\sqrt{34}=c\longrightarrow$ simplify $2w\sqrt{34}=c$
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