Pythagorean Theorem Finding Length

The Pythagorean Theorem is one of the most famous mathematical formulas out there. It's a fundamental theorem in geometry that establishes the relationship between the lengths of the sides of a right triangle. In this article, we'll talk about how to use the Pythagorean Theorem to find the length of a side, expressed in centimeters (cm).

What Is the Pythagorean Theorem?

The Pythagorean Theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. Put simply, it means that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

This theorem can be expressed algebraically as a^2 + b^2 = c^2, where a and b are the lengths of the two legs, and c is the length of the hypotenuse.

How to Use the Pythagorean Theorem

The Pythagorean Theorem can be used to find the length of any side of a right triangle, as long as you know the lengths of the other two sides. Here's how to do it:

1. Identify which side you want to find the length of. Let's call it x.
2. Determine which sides of the right triangle are the legs and which is the hypotenuse.
3. Plug in the lengths of the legs and the hypotenuse into the Pythagorean formula: a^2 + b^2 = c^2.
4. Solve for x by isolating it on one side of the equation and taking the square root: x = sqrt(c^2 - a^2) or x = sqrt(c^2 - b^2).

Example Problem:

Suppose you have a right triangle with legs measuring 5 cm and 12 cm. What is the length of the hypotenuse?

1. Identify the hypotenuse as x.
2. The legs are 5 cm and 12 cm.
3. Plug in the values into the formula: 5^2 + 12^2 = x^2.
4. Simplify: x^2 = 169.
5. Solve for x: x = sqrt(169) = 13 cm.

So the length of the hypotenuse is 13 cm.

Get Your Pythagorean Theorem Example in DOCX Format

Need more practice using the Pythagorean Theorem to find the length of a leg or hypotenuse? Download our Pythagorean Theorem example in DOCX format now and practice your skills with detailed solutions provided. It's a great tool for both students and teachers looking to master this crucial concept in geometry.

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