https://file.aiquickdraw.com/mathbot/file/1729356303624garsckj0.jpg

Let's analyze problem #6.

The triangle in #6 is a 45°-45°-90° triangle, which means it's an isosceles right triangle. In such triangles, the lengths of the two legs are equal, and the hypotenuse is \( x\sqrt{2} \), where \( x \) is the length of each leg.

Given:
- Hypotenuse = \( 5\sqrt{2} \)

Since the hypotenuse in a 45°-45°-90° triangle is \( x\sqrt{2} \), we can set up the equation:
\[
x\sqrt{2} = 5\sqrt{2}
\]

To find \( x \), divide both sides by \( \sqrt{2} \):
\[
x = 5
\]

Thus, the length of each leg \( x \) is **5**.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. How would you find the hypotenuse of a 45°-45°-90° triangle if both legs are known?
2. What is the general formula for the sides of a 45°-45°-90° triangle?
3. How would you solve for the leg length if you were given the hypotenuse as 10?
4. What properties make a 45°-45°-90° triangle different from other right triangles?
5. How can you determine if a triangle is a 45°-45°-90° triangle by only knowing the angles?

**Tip:** In a 45°-45°-90° triangle, remember that if you know one leg, you can always find the hypotenuse by multiplying the leg by \( \sqrt{2} \).

Find x in a 45°-45°-90° triangle with hypotenuse 5√2.

Learn how to solve a 45°-45°-90° triangle problem where the hypotenuse is given as 5√2. Discover the key geometry concepts and theorems used to determine the leg length in this special triangle. 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