Discussion
The base of a right triangle is 8 and hypotenuse is 10. Its area is?
Answer: D
Find the missing perpendicular side by Pythagoras.
\[ \text{height} = \sqrt{10^{2} - 8^{2}} = \sqrt{100 - 64} = \sqrt{36} = 6 \]
\[ A = \frac{1}{2} \times 8 \times 6 = 24 \]
The hypotenuse is never a side of the right angle, so it cannot be used as a height - using 8 and 10 as the two legs would give 40.
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