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Solution of the Week #504 - Sum and Product

February 10, 2025 Elliott Line

By Pythagoras the long side of the triangle is 87. Since a+b is 100 we can change b to 100-a. The small triangle at the top shares an angle with the large triangle, and since both are also right-angled the two triangles are similar.

87/63 = (63-a)/(a-13)

87(a-13) = 63(63-a)

87a-1131 = 3969-63a

150a = 5100

a = 34

b = 100-a = 66

a*b = 34*66 = 2244

← Solution of the Week #505 - Linked ValuesSolution of the Week #503 - Semicircle in a Triangle →

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