Question

r Two Isosceles triangles have equal vertical angles and their areas are in the ratio 36:25 find then ratio of their corresponding height.

Answer 1

Let in 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).