The base of a right - angled triangle measures 48 cm and its hypotenuse measures 50 cm . Find the area of the triangle .

Explanation

To find the area of the right-angled triangle with a base of 48 cm and a hypotenuse of 50 cm, we will follow these steps:

### Step 1: Identify the known values
We know:
- Base (b) = 48 cm
- Hypotenuse (h) = 50 cm

### Step 2: Use the Pythagorean theorem to find the height
In a right-angled triangle, the Pythagorean theorem states that:
\[ h^2 = b^2 + p^2 \]
where \( p \) is the height of the triangle.

Substituting the known values:
\[ 50^2 = 48^2 + p^2 \]

Calculating the squares:
\[ 2500 = 2304 + p^2 \]

### Step 3: Solve for the height (p)
Rearranging the equation to find \( p^2 \):
\[ p^2 = 2500 - 2304 \]
\[ p^2 = 196 \]

Now, take the square root to find \( p \):
\[ p = \sqrt{196} \]
\[ p = 14 \text{ cm} \]

### Step 4: Calculate the area of the triangle
The area \( A \) of a right-angled triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

Substituting the values we have:
\[ A = \frac{1}{2} \times 48 \times 14 \]

Calculating the area:
\[ A = 24 \times 14 \]
\[ A = 336 \text{ cm}^2 \]

### Final Answer
The area of the triangle is \( 336 \text{ cm}^2 \).

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