Triangle ABC is isosceles with AB = BC. If AB = 20 and [ABC] = 240, then find the perimeter of triangle ABC.
+15000 Triangle ABC is isosceles with AB = BC. If AB = 20 and [ABC] = 240, then find the perimeter of triangle ABC.
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\(\beta=360°-240°=120°\)
\(b^2=a^2+c^2-2ac\ cos\beta\)
\(b^2=20^2+20^2-2\cdot 20\cdot 20\cdot \ cos\ 120°\)
\(b^2=1200\)
\(b=\sqrt{1200}\)
\(b=34.641\)
\(P=a+c+b=20+20+34.641\)
\(P=74.641\)
The perimeter of triangle ABC is 74.641
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