https://file.aiquickdraw.com/mathbot/file/17260835427756e6mtopl.jpg

The problem shown in the image is written in Dutch, and it translates to:

"The hypotenuse of an isosceles right triangle is 5 cm. Calculate, to an accuracy of 0.1 cm, the length of the legs of the triangle."

### Solution:
In an isosceles right triangle, the two legs have equal lengths, and the hypotenuse relates to the legs by the Pythagorean theorem:

\[
c^2 = a^2 + a^2 = 2a^2
\]
where:
- \( c \) is the hypotenuse (5 cm in this case),
- \( a \) is the length of each leg.

To find \( a \), we rearrange the formula:

\[
c^2 = 2a^2 \quad \Rightarrow \quad a^2 = \frac{c^2}{2} \quad \Rightarrow \quad a = \frac{c}{\sqrt{2}}
\]

Substituting \( c = 5 \, \text{cm} \):

\[
a = \frac{5}{\sqrt{2}} \approx \frac{5}{1.414} \approx 3.54 \, \text{cm}
\]

Thus, the length of each leg is approximately **3.5 cm** (to the nearest 0.1 cm).

---

Would you like any further details on this problem? Here are some related questions you might find helpful:

1. How is the Pythagorean theorem derived?
2. Can the Pythagorean theorem apply to all types of triangles?
3. How do you calculate the area of an isosceles right triangle?
4. What is the significance of the 45°-45°-90° triangle in trigonometry?
5. How would this problem change if the hypotenuse was different?

**Tip**: In an isosceles right triangle, the angles are always 45°, 45°, and 90°, making calculations involving the sides quite efficient.

De schuine zijde van een gelijkbenige rechthoekige driehoek is 5 cm. Bereken, op 0,1 cm nauwkeurig, de lengte van de rechthoekszijden.

Learn how to calculate the length of the legs of an isosceles right triangle with a 5 cm hypotenuse using the Pythagorean theorem. Suitable for students in Grades 6-8, this problem provides a step-by-step solution, accurate to 0.1 cm.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation