https://file.aiquickdraw.com/mathbot/file/1726403422345qrz22zre.jpg

This problem involves a right triangle where the length of one leg is 10 cm, the height of the triangle is 4.5 cm, and the length of the other leg is 7 cm. We are tasked with finding the length of the hypotenuse, \(x\).

To solve this, we can use the Pythagorean theorem, which states:

\[
a^2 + b^2 = c^2
\]

Where:
- \(a\) and \(b\) are the legs of the right triangle, and 
- \(c\) is the hypotenuse.

However, in this case, the triangle is split into two right triangles. We will first solve for \(x\) by applying the Pythagorean theorem in two steps.

1. Consider the right triangle with legs 10 cm and 4.5 cm. Here, we can find the length of the hypotenuse (which will contribute to the total length \(x\)).

Let's calculate it.The length of the hypotenuse (which represents \(x\) for the first right triangle with legs 10 cm and 4.5 cm) is approximately 10.97 cm.

Do you need more details, or have any questions about this? 

Here are 5 related questions for practice:
1. How do you apply the Pythagorean theorem to other right triangles?
2. How would the solution change if the height of the triangle were different?
3. What if the triangle had different leg lengths, how would you approach the problem?
4. Can you calculate the perimeter of the triangle given the length of \(x\)?
5. How does trigonometry relate to this type of problem?

**Tip:** When solving right triangle problems, always ensure you know which sides are the legs and which is the hypotenuse to avoid errors with the Pythagorean theorem.

Work out the value of x in the given triangle with legs of 10 cm, 7 cm, and height of 4.5 cm.

Find the value of the hypotenuse (x) in a triangle where the legs are 10 cm, 7 cm, and the height is 4.5 cm. Learn how to apply the Pythagorean theorem step by step. Suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation