Question

Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm.

• A. 25
• B. 30
• C. 5
• D. 15

Answer 1

The Correct Option is B

Step 1: Use the Pythagorean theorem to find the height of the triangle: 

\[ \text{Hypotenuse}^2 = \text{Base}^2 + \text{Height}^2 \]

\[ 13^2 = 12^2 + \text{Height}^2 \]

\[ 169 = 144 + \text{Height}^2 \]

Step 2: Solving for the height:

\[ \text{Height}^2 = 169 - 144 = 25 \]

\[ \text{Height} = 5 \text{ cm} \]

Step 3: The area of the triangle is:

\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]

\[ = \frac{1}{2} \times 12 \times 5 = 30 \text{ cm}^2 \]