Solve. Round to the nearest tenth.

Find the perimeter of a right triangle with legs that measure 7 in. and 24 in.

To find the perimeter of a right triangle, we first need to calculate the length of the hypotenuse using the Pythagorean theorem. The theorem states:

\[
c = \sqrt{a^2 + b^2}
\]

Where \(a\) and \(b\) are the lengths of the legs of the triangle, and \(c\) is the length of the hypotenuse.

Given:
- \(a = 7\) inches
- \(b = 24\) inches

Let's calculate the hypotenuse:

\[
c = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25 \text{ inches}
\]

Now, we can find the perimeter of the triangle by adding the lengths of the two legs and the hypotenuse:

\[
\text{Perimeter} = 7 + 24 + 25 = 56 \text{ inches}
\]

Thus, the perimeter of the triangle is **56 inches**.

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:
1. How would the perimeter change if one leg were doubled?
2. Can you apply the Pythagorean theorem in a non-right triangle?
3. What if the triangle had a hypotenuse of 26 inches—how would the legs change?
4. How do you find the area of this right triangle?
5. What other methods can be used to find the perimeter of a triangle?

**Tip:** In any right triangle, the Pythagorean theorem is key to finding the hypotenuse or missing side.

Find the perimeter of a right triangle with legs that measure 7 in. and 24 in.

Learn how to find the perimeter of a right triangle with legs measuring 7 inches and 24 inches using the Pythagorean theorem. This problem walks you through the step-by-step calculation of the hypotenuse and the perimeter. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation