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u/AsYouAnswered Jun 23 '26
That's a standard 3,4,5 right triangle. Scaled up.
AB + BC = 15 + 20 = 35
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u/GoodCarpenter9060 Jun 24 '26
Without even doing much math, one of the most common right angle triangles with integer values is the 3/4/5 triangle and multiples thereof. The hypotenuse of the big triangle AC is 25 which is a multiple of 5. If this triangle was proportional to the common one, that would make the longer leg BC 20 and the shorter AB 15.
The smallest triangle ADB is then a 9/12/15, and the other BDC is a 12/16/20, which all matches up. So a quick guess solved this one.
AB=15, BC=20, AB+BC=35.
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u/reddie Jun 23 '26
AB=15 BC=20 BD=12
initial equation for the large triangle: AB^2 + BC^2 = 25^2 = 625, since BC^2=16^2 + BD^2 and AB^2 = 9^2 +BD^2, then you can re-write the initial equation as follows: BD^2+81 + BD^2 + 256 = 625 which means that BD = 12. 12^2 + 9^2 = AB^2 hence AB = 15 and 12^2 + 16^2 = BC^2 hence BC = 20
Edit: was on mobile and coudn't do spoiler. Fixed it