The base of a right angled triangle is 5 metres and hypotenuse is 13 metres. Its area will be -----

Options

A. `25 m^2`
B. `28 m^2`
C. `30 m^2`
D. None of these

Answer

To find the area of the right-angled triangle with a base of 5 meters and a hypotenuse of 13 meters, we will follow these steps:

### Step 1: Identify the known values
We know:
- Base (b) = 5 meters
- Hypotenuse (h) = 13 meters

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

### Step 3: Substitute the known values into the theorem
Substituting the known values:
\[ 13^2 = 5^2 + p^2 \]

### Step 4: Calculate the squares
Calculating the squares:
\[ 169 = 25 + p^2 \]

### Step 5: Solve for \( p^2 \)
Rearranging the equation to solve for \( p^2 \):
\[ p^2 = 169 - 25 \]
\[ p^2 = 144 \]

### Step 6: Find the value of \( p \)
Taking the square root of both sides to find \( p \):
\[ p = \sqrt{144} \]
\[ p = 12 \text{ meters} \]

### Step 7: 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:
\[ A = \frac{1}{2} \times 5 \times 12 \]

### Step 8: Perform the multiplication
Calculating the area:
\[ A = \frac{1}{2} \times 60 \]
\[ A = 30 \text{ square meters} \]

### Final Answer
The area of the right-angled triangle is **30 square meters**.

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