# Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of their corresponding heights is

**Question:**

Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of their corresponding heights is

(a) 4 : 5

(b) 5 : 4

(c) 3 : 2

(d) 5 : 7

**Solution:**

Given: Two isosceles triangles have equal vertical angles and their areas are in the ratio of 16:25.

To find: Ratio of their corresponding heights.

Let ∆ABC and ∆PQR be two isosceles triangles such that ∠A=∠P. Suppose AD ⊥ BC and PS ⊥ QR .

In ∆ABC and ∆PQR,

ABPQ=ACPR∠A=∠P∴∆ABC~∆PQR SAS similarity

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

Hence,

Ar∆ABCAr∆PQR=ADPS2⇒1625=ADPS2⇒ADPS=45

Hence we got the result as $(a)$

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