https://file.aiquickdraw.com/mathbot/file/1727311780318vdhz5k1p.jpg

The problem is asking for the side length \( s \) of an isosceles right triangle, given that its area is \( 50 \, \text{cm}^2 \).

### Step-by-Step Solution:

1. **Formula for the Area of an Isosceles Right Triangle**:
   The area \( A \) of a triangle is given by:
   \[
   A = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   In an isosceles right triangle, the base and height are the same, so if \( s \) is the length of one leg, the formula becomes:
   \[
   A = \frac{1}{2} \times s \times s = \frac{s^2}{2}
   \]

2. **Given Area**:
   We are given that the area is \( 50 \, \text{cm}^2 \):
   \[
   \frac{s^2}{2} = 50
   \]

3. **Solve for \( s \)**:
   Multiply both sides of the equation by 2:
   \[
   s^2 = 100
   \]
   Take the square root of both sides:
   \[
   s = \sqrt{100} = 10 \, \text{cm}
   \]

### Conclusion:
The value of \( s \) is \( 10 \, \text{cm} \).

---

Do you need any further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. What is the perimeter of the isosceles right triangle with side length \( s = 10 \, \text{cm} \)?
2. How would the area change if the side length \( s \) is doubled?
3. What is the hypotenuse of this isosceles right triangle with \( s = 10 \, \text{cm} \)?
4. How does the area of an equilateral triangle with the same side length compare to this isosceles triangle?
5. What is the formula for the area of a general right triangle?

**Tip**: In an isosceles right triangle, the ratio of the sides is always \( 1:1:\sqrt{2} \).

The area of an isosceles right triangle is 50 cm². What is the value of s?

Learn how to calculate the side length of an isosceles right triangle with a given area of 50 cm². This step-by-step solution uses basic geometry and algebra concepts, including the formula for the area of a triangle and solving quadratic equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation