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Chapter 1: Q. 4 (page 13)

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.

Short Answer

Expert verified

The given triangle is a right triangle because612=112+602.

Step by step solution

01

Step 1. Given information.

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

02

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:

612=3721

The sum of squares of the other two sides is:

602+112=3600+121=3721

03

Step 3. Conclusion.

The given triangle is a right triangle because612=112+602.

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