Question

two isoceles triangle have equal angles and their areas are in the ratio 16: 25 find the ratio of their corresponding height ​

Answer 1

Answer:

4:5

Step-by-step explanation:

Let the two isosceles triangles be  ΔABC and ΔPQR with ∠A = ∠P.

Therefore,

AB/AC = PQ/PR

In ΔABC and ΔPQR,

∠A = ∠P   (given)

AB/AC = PQ/ PR (sides of a isosceles∆)

ΔABC – ΔPQR  

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.

ar(ΔABC)/ar(ΔPQR) = (AD/PS)²

16/25 = (AD/PS)²

√16/25 = √(AD/PS)²

AD/ PS = 4/5

AD : PS = 4 : 5

Hence, the ratio of their corresponding heights is 4 : 5.