In a right triangle, if a and b are the measures of the legs and c is the measure of the hypotenuse, then a^{2} + b^{2} = c^{2}.

Video Examples: The Pythagorean Theorem

Example of Pythagorean Theorem

The right triangle shown has legs 3 and 4 and hypotenuse 5.

Solved Example on Pythagorean Theorem

Ques: The radius of the circle is 4 inches. Find the length of side of the square using Pythagorean theorem.

Choices:

A. 4 inches
B. 8 inches
C. inches
D. inches
Correct Answer: D

Solution:

Step 1: Radius of the circle = 4 inches.
Step 2: Hypotenuse = 2 × 4 = 8 inches.
Step 3: Let s be the side of the triangle. Then s is the base of the right triangle.
Step 4: Pythagorean Theorem states that 'In a right triangle, if a and b are the measures of the legs and c is the measure of the hypotenuse, then a^{2} + b^{2} = c^{2}.
Step 5: Using Pythagorean Theorem,we get,