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In a right-angled triangle the hypotenuse is $13$ cm and one of the legs is $5$ cm. Find the area of the triangle.
A$25$ cm²
B$30$ cm²
C$32.5$ cm²
D$60$ cm²
Answer & Solution
Correct answer: B. $30$ cm²
**Find the other leg.** By Pythagoras: $\text{other leg} = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12$ cm.
**Area.** $\dfrac{1}{2} \times 5 \times 12 = 30$ cm².
**Why option C (32.5) is tempting.** Picking the *hypotenuse* and the given leg as base × height gives $\tfrac{1}{2} \times 13 \times 5 = 32.5$. But the two perpendicular sides in a right triangle are the *legs*, not the hypotenuse.
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