The base of a right angled triangle is 8 cm and hypotenuse is 17 cm . Find its area.

Answer

To find the area of a right-angled triangle with a base of 8 cm and a hypotenuse of 17 cm, we can follow these steps:

### Step 1: Identify the given values
- Base (b) = 8 cm
- Hypotenuse (h) = 17 cm

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

Substituting the known values:
\[ 17^2 = 8^2 + p^2 \]

### Step 3: Calculate the squares
Calculating the squares:
- \( 17^2 = 289 \)
- \( 8^2 = 64 \)

So, we have:
\[ 289 = 64 + p^2 \]

### Step 4: Rearrange the equation to solve for \( p^2 \)
Subtract \( 64 \) from both sides:
\[ p^2 = 289 - 64 \]
\[ p^2 = 225 \]

### Step 5: Find the height (perpendicular)
Now, take the square root of both sides to find \( p \):
\[ p = \sqrt{225} \]
\[ p = 15 \, \text{cm} \]

### Step 6: 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:
\[ A = \frac{1}{2} \times 8 \times 15 \]

### Step 7: Simplify the area calculation
Calculating:
\[ A = \frac{1}{2} \times 8 = 4 \]
\[ A = 4 \times 15 = 60 \, \text{cm}^2 \]

### Final Answer
The area of the triangle is \( 60 \, \text{cm}^2 \).

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