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Triangle ABC is isosceles with AB = BC  If AC = 20 and [ABC] = 240, then find the perimeter of triangle ABC.

 

I think it's maybe Heron's Formula? I've been trying it but I keep getting confused with all the square roots and everyone is giving me different answers. I don't know hich one to trust. Any help would be AMAZING and will mean a WHOLE LOT to me.

 Jul 18, 2020
 #1
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Area of triangle =[Base x Height ]/ 2

 

240 = [20 x Height] / 2

Height =480 / 20

Height = 24

Draw a perpendicular line to AC

AC/2 =10 - This divides the triangle into 2 congruent triangles.

The height of each of these 2 triangles =24 and the base of each =10

Using Pythagoras's Theorem:

24^2 + 10^2 =AB^2 =BC^2

AB^2 =576 + 100 =676      Take the sqrt of both sides

AB = 26 = BC

The perimeter =26 + 26 + 20 = 72

 Jul 18, 2020
 #2
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Thank you so much!!!! I was able to solve it myself using the first few lines that you gave me! There are a bunch of trolls on this website that just post completely wrong answers. Thank you!

Guest Jul 20, 2020

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