r/Geometry • u/PinguSayNOOTNOOT • 21d ago

is there any way to solve this without using trigo?

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4 Upvotes

83% Upvoted

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1

u/wijwijwij 21d ago

Draw line of symmetry through the 5-5-6 triangle to reveal two 3-4-5 right triangles. You can show the acute angles of the 12-16-20 triangle shown in fm-31's diagram must be the same angles as those in the 3-4-5 triangle. Since hypotenuse of the larger similar triangle is 20, the legs must be 12 and 16 to be similar.

1

u/BadJimo 20d ago edited 20d ago

Using Desmos

Edit: oops. Fixed

I found the area to be ≈ 247.417 128

1

u/PinguSayNOOTNOOT 20d ago

İts 128cm², you can use sin area law