Question

two isosceles triangles have equal vertical angles and their area in ratio 25:36. Find the ratio of their corresponding heights.​

Answer 1

Step-by-step explanation:

Δ ABC with height as AD,

AB = AC

⇒ ∠B = ∠C = 180-∠A/2...... Equation-1

And in Δ PQR with height as PS

PQ = PR

⇒ ∠Q = ∠R = 180-∠P/2...... Equation- 2

Given vertical angles of the two triangles are equal.

i.e., ∠A = ∠P

and ∠B = ∠C = ∠Q = ∠R

By AAA similarity criterion,

We know ratio between the areas of two similar triangle is same as the ratio between the square of their corresponding altitudes.

And corresponding heights of two given triangles are AD and PS.

Area of Δ ABC/Area of Δ PQR = AD²/PS²

= 36²/25² = AD²/PS²

AD : PS = 6 : 5 ( ratio of their corresponding heights).

hope it helps you......