The base of a right angled triangle is `48 cm` and its hypotenuse is `50 cm` then its area is

Options

A. `150cm^(2)`
B. `336cm^(2)`
C. `300cm^(2)`
D. `475cm^(2)`

Answer

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

### Step 1: Identify the sides of the triangle
Given:
- Base (BC) = 48 cm
- Hypotenuse (AC) = 50 cm

Let the height (AB) be the unknown side we need to find.

### Step 2: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
Substituting the known values:
\[ 50^2 = AB^2 + 48^2 \]

### Step 3: Calculate the squares
Calculating the squares:
\[ 50^2 = 2500 \]
\[ 48^2 = 2304 \]

### Step 4: Rearrange the equation
Now, substituting the squares back into the equation:
\[ 2500 = AB^2 + 2304 \]
To find \( AB^2 \), rearrange the equation:
\[ AB^2 = 2500 - 2304 \]

### Step 5: Perform the subtraction
Calculating the right side:
\[ AB^2 = 196 \]

### Step 6: Find the height (AB)
To find \( AB \), take the square root of both sides:
\[ AB = \sqrt{196} = 14 \text{ cm} \]

### Step 7: Calculate the area of the triangle
Now that we have both the base and height, we can calculate the area using the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Substituting the values:
\[ \text{Area} = \frac{1}{2} \times 48 \times 14 \]

### Step 8: Perform the multiplication
Calculating the area:
\[ \text{Area} = \frac{1}{2} \times 672 = 336 \text{ cm}^2 \]

Thus, the area of the triangle is **336 cm²**.

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