Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

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.

Step-by-Step Solution

Answer

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

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 ${\left(61\right)}^2={\left(11\right)}^2+{\left(60\right)}^2$.