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### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Use the converse of the Pythagorean Theorem to show that a triangle whose sides are of lengths 11, 60, and 61 is a right triangle.

The given triangle is a right triangle because ${\left(61\right)}^{2}={\left(11\right)}^{2}+{\left(60\right)}^{2}$.

See the step by step solution

## Step 1. Given information.

The lengths of a triangle are 11, 60 and 61.

## Step 2. Show that the triangle is a right triangle.

Converse of the Pythagorean Theorem: In a triangle, if the square of the length of one side equals the sum of the squares of the lengths of the other two sides, the triangle is a right triangle.

The square of the largest side is:

${\left(61\right)}^{2}=3721$

The sum of squares of the other two sides is:

$\begin{array}{rcl}{\left(60\right)}^{2}+{\left(11\right)}^{2}& =& 3600+121\\ & =& 3721\end{array}$

## Step 3. Conclusion.

The given triangle is a right triangle because ${\left(61\right)}^{2}={\left(11\right)}^{2}+{\left(60\right)}^{2}$.