In a triangle ABC, AB = 8 cm, AC = 10 cm and `angleB = 90^(@)`, then the area of `Delta ABC` is

Options

A. 49 sq. cm
B. 36 sq. cm
C. 25 sq. cm
D. 24 sq. cm

Answer

To find the area of triangle ABC where AB = 8 cm, AC = 10 cm, and angle B = 90°, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the triangle type**: Since angle B is 90°, triangle ABC is a right-angled triangle with AB and BC as the two legs, and AC as the hypotenuse.

2. **Use the Pythagorean theorem**:
- According to the Pythagorean theorem, in a right triangle:
\[ AC^2 = AB^2 + BC^2 \]
- Here, we know:
- \( AC = 10 \, \text{cm} \)
- \( AB = 8 \, \text{cm} \)
- We need to find BC. Rearranging the formula gives us:
\[ BC^2 = AC^2 - AB^2 \]

3. **Calculate BC**:
- Substitute the known values:
\[ BC^2 = 10^2 - 8^2 \]
\[ BC^2 = 100 - 64 \]
\[ BC^2 = 36 \]
- Taking the square root:
\[ BC = \sqrt{36} = 6 \, \text{cm} \]

4. **Calculate the area of triangle ABC**:
- The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
- Here, we can take:
- Base = BC = 6 cm
- Height = AB = 8 cm
- Substitute these values into the area formula:
\[ A = \frac{1}{2} \times 6 \times 8 \]
\[ A = \frac{1}{2} \times 48 = 24 \, \text{cm}^2 \]

### Final Answer:
The area of triangle ABC is \( 24 \, \text{cm}^2 \).

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