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Find the area of triangle ABC

 

 Jul 5, 2023
 #1
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Let CH ==y
Let AH ==x
Let CB ==z


x^2 + y^2=18^2...................(1)  
15^2 + y^2==z^2.................(2)   
z^2 + 18^2=(15 + x)^2..   ....(3), solve for x, y, z 

 

x ==12,  y==6*sqrt(5),  z=9*sqrt(5)


Area of ABC==1/2 * (12+15) * 6*sqrt(5)==181.1215 u^2

 Jul 5, 2023
 #2
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here's a hint!

try using the 30-60-90 triangle rule!

 Jul 5, 2023
 #3
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what?!? the question never tooks about the angles and the altitude of a right triangle where the altitude goes through the right angle does not always suggest that it forms a 30-60-90 triangle. Think about it. @Guest is right here.

SoulKingBrook  Jul 6, 2023

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