Find the area of a right triangle whose hypotenuse is 26 cm long and one of the sides containing the right angle measures 10 cm .

Answer

To find the area of a right triangle with a hypotenuse of 26 cm and one side measuring 10 cm, we can follow these steps:

### Step 1: Identify the sides of the triangle
Let’s denote the triangle as ABC, where:
- BC is the hypotenuse (26 cm)
- AC is one side (10 cm)
- AB is the other side (which we need to find)

### Step 2: Use the Pythagorean theorem
According to the Pythagorean theorem:
\[ BC^2 = AB^2 + AC^2 \]
Substituting the known values:
\[ 26^2 = AB^2 + 10^2 \]

### Step 3: Calculate the squares
Calculate \( 26^2 \) and \( 10^2 \):
\[ 676 = AB^2 + 100 \]

### Step 4: Rearrange the equation to find AB²
Now, we can rearrange the equation to solve for \( AB^2 \):
\[ AB^2 = 676 - 100 \]
\[ AB^2 = 576 \]

### Step 5: Take the square root to find AB
Now, take the square root of both sides to find AB:
\[ AB = \sqrt{576} \]
\[ AB = 24 \text{ cm} \]

### Step 6: Calculate the area of the triangle
The area \( A \) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, we can take:
- Base = AB = 24 cm
- Height = AC = 10 cm

Substituting the values:
\[ A = \frac{1}{2} \times 24 \times 10 \]
\[ A = \frac{240}{2} \]
\[ A = 120 \text{ cm}^2 \]

### Final Answer:
The area of the right triangle is **120 cm²**.

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