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UKMT Intermediate Mathematical Challenge, 2023

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The sum of the lengths of the three sides of a right-angled triangle is 16 cm. The sum of the squares of the lengths of the three sides of the triangle is $98\text{ cm}^2$ . What is the area, in $\text{cm}^2$ , of the triangle?

(A) $8$ (B) $10$ (C) $12$ (D) $14$ (E) $16$

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