Question

In triangle \( ABC \), if \( AB = 6 \), \( BC = 8 \), and \( AC = 10 \), what is the area of the triangle?

• A. \( 24 \)
• B. \( 25 \)
• C. \( 26 \)
• D. \( 27 \)
• E. \( 28 \)

Hint:

For right triangles, use the formula \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). You can identify a right triangle by checking if \( a^2 + b^2 = c^2 \), where \( a \), \( b \), and \( c \) are the sides.

Answer 1

The Correct Option is A

The given triangle has side lengths \( AB = 6 \), \( BC = 8 \), and \( AC = 10 \). This is a right triangle, since \( 6^2 + 8^2 = 36 + 64 = 100 = 10^2 \). Step 1: Use the formula for the area of a right triangle: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}. \] Here, we can take \( AB = 6 \) as the base and \( BC = 8 \) as the height. Step 2: Calculate the area: \[ \text{Area} = \frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times 48 = 24. \] Thus, the area of the triangle is \( 24 \).