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Triangle ABC is isosceles with AB=AC and...

Triangle `ABC` is isosceles with `AB=AC and BC=65cm.` P is a point on `BC` such that the perpendiculardistances from P to `AB and AC` are `24cm and 36cm,` respectively. The area of triangle `ABC` (in sq cm is)

A

8

B

12

C

16

D

6

Text Solution

Verified by Experts

The correct Answer is:
D

Clearly, `AP = A'P' = 3, BP = AP' = 4 and PC = P' C = 5`
So, `angle CPP' = angle PP'C = 60^(@)`
So, PCp' is equilateral and thus PP' = 5
So, `angle PAP' = 90^(@) " " [ :' AP = 3, PP' = 5]`
`:.` Area of `DeltaAPP' = (1)/(2) (3) (4) = 6`
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