SOLUTION: In an acute triangle ABC,an altitude AD is drawn. Find the area of triangle ABC if AB=15, AC=18, and BD=10.

Algebra ->  Triangles -> SOLUTION: In an acute triangle ABC,an altitude AD is drawn. Find the area of triangle ABC if AB=15, AC=18, and BD=10.      Log On


   

Question 668359: In an acute triangle ABC,an altitude AD is drawn. Find the area of triangle ABC if AB=15, AC=18, and BD=10.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Since AD is the altitude to base BC we have to find AD & DC
Two right triangles are formed .
ABD & ACD
In triangle ABD
BD= 10
AB= 15
Apply Pythagoras theorem
AB is the hypotenuse
15%5E2-10%5E2=+AD%5E2
225-100=AD^2
125 = AD^2
AD+=+5+sqrt%285%29
We have AC= 18
AD= 5sqrt%285%29
DC%5E2=+18%5E2-%285sqrt%285%29%29%5E2
DC%5E2=324-125
DC%5E2=199
DC+=+sqrt%28199%29
BD+DC= BC
BC+=+10+%2Bsqrt%28199%29
Area of triangle = 1/2 base * altitude
=1%2F2+%2A+%2810%2Bsqrt%28199%29%29%2A5sqrt%285%29
By using calculator you will get 134.76 sq. cm