Question

26)
Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. Find the ratio of their corresponding
sides. ​

Answer 1

Answer:

4/5

Step-by-step explanation:

Let the triangles be ΔABC and ΔDEF

Let ∠A = ∠D and AB = AC and DE = DF(as per the question)

Thus, in ΔABC, by ASP,

∠A + ∠B + ∠C = 180

∠A - 2∠B = 180 (∠B = ∠C)

∠A = 180 + 2∠B

Similarly in ΔDEF, ∠D = 180 + 2∠E

But we know ∠A = ∠D

So, 180 + 2∠B = 180 + 2∠E

2∠B = 2∠E

∠B = ∠E

So, now in triangles ΔABC and ΔDEF,

By AA similarity criterion, ΔABC ∾ ΔDEF

AB/DE = BC/EF = AC/DF

Areas of similar triangles are in ratio to the squares of their corresponding sides.

ar(ΔABC)/ar(ΔDEF) = 16/25 = AB²/DE²

AB/DE = $\sqrt{\frac{16}{25} }$

AB/DE = 4/5