Question

Two isosceles triangles have equal vertical angles and their areas are in the ratio
9 : 16. Find the ratio of their corresponding heights

Answer 1

Step-by-step explanation:

Let ABC,PQR be two isosceles triangle with equal vertical angles.

Let in ΔABC,AB=AC

⇒∠B=∠C=

2

180−∠A

And in ΔPQR,PQ=PR

⇒∠Q=∠R=

2

180−∠P

Given two vertical angles are equal.

∴∠A=∠P

⇒∠B=∠C=∠Q=∠R

By AAA postulate,

∴ΔABC∼ΔPQR

.

AreaofΔPQR

AreaofΔABC

=

PS

2

AD

2

⇒

16

9

=

PS

2

AD

2

⇒AD:PS=3:4