Question:
In triangle \( ABC \), if \( AB = 6 \), \( BC = 8 \), and \( AC = 10 \), what is the area of the triangle?
In triangle \( ABC \), if \( AB = 6 \), \( BC = 8 \), and \( AC = 10 \), what is the area of the triangle?
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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.
Updated On: Oct 6, 2025
- \( 24 \)
- \( 25 \)
- \( 26 \)
- \( 27 \)
- \( 28 \)
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The Correct Option is A
Solution and Explanation
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 \( 24 \).
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