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Triangle $ABC$ is isosceles with $AB = BC.$  If $AC = 20$ and $[ABC] = 100 \sqrt{3},$ then find the perimeter of triangle $ABC.$

 Dec 20, 2023
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                        B

 

 

 A                  20                         C

 

The altitude is

 

100 sqrt (3)  = (1/2) (20) (altitude)

 

100 sqrt (3) = 10 (altitude)             divide both sides by 10

 

10sqrt (3) = altitude =  sqrt (300)

 

Call the altitude BD

DC = 10

BC= ????

 

Since the triangle issoceles, the altitude bisects the base 

So  by the Pythagorean Theorem

 

VC = sqrt ( DC^2 + BD^3) 

 

BC =  sqrt ( 10^2  + (sqrt 300)^2 ] =  sqrt [ 400]  =  20

 

The perimeter  =  AB + BC + AC =   20 + 20 + 20  =  60

 

 

cool cool cool

 Dec 20, 2023
edited by CPhill  Dec 20, 2023

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