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

Answer

To find the area of the right-angled triangle given the base and hypotenuse, we can follow these steps:

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

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

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ 50^2 = p^2 + 48^2 \]

### Step 4: Calculate the squares
Calculate \( 50^2 \) and \( 48^2 \):
- \( 50^2 = 2500 \)
- \( 48^2 = 2304 \)

### Step 5: Set up the equation
Now we can set up the equation:
\[ 2500 = p^2 + 2304 \]

### Step 6: Solve for \( p^2 \)
Rearranging the equation to find \( p^2 \):
\[ p^2 = 2500 - 2304 \]
\[ p^2 = 196 \]

### Step 7: Calculate \( p \)
Taking the square root of both sides gives us:
\[ p = \sqrt{196} = 14 \text{ cm} \]

### Step 8: Calculate the area of the triangle
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Substituting the values we have:
\[ A = \frac{1}{2} \times 48 \times 14 \]

### Step 9: Perform the calculations
Calculating the area:
\[ A = \frac{1}{2} \times 48 \times 14 = 24 \times 14 = 336 \text{ cm}^2 \]

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

---