UKMT - Senior Mathematical Challenge - 2022 - 23 | Exact Science

23

Three squares ABC, DEF, and GHI have vertices which sit on the sides of triangle JKL as shown. The squares have areas of 10, 90, and 40, respectively. What is the area of triangle JKL?

A. 220.5 B. 21 × √10 C. 252 D. 21 × √10 E. 441/10

Answer

A

SOLUTIOn

By calculating the lengths and areas of the squares and using geometric relationships, the area of the triangle is found to be 220.5.

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