Given : - AB = AC, PQ = PR and <A = <P

And AD and PS are altitudes

And, Area (ΔABC)/Area of( ΔPQR) = 36/25………………..(i)

To find: AD/PS

Proof:- Since, AB = AC and PQ = PR

Then, AB/AC = 1 and PQ/PR = 1

So, AB/AC = PQ/PR

Or, AB/PQ = AC/PR……………….(ii)

In ΔABC and ΔPQR

<A = <P (Given)

AB/PQ = AC/PR (From equation ii)

Then, ΔABC ~ ΔPQR (BY AA similarity)

So, Area of ΔABC/Area of ΔPQR = AB² /PQ²…..(iii) (By area of similar triangle)

Compare equation I and II

AB²/PQ² = 36/25

Or, AB/PQ = 6/5

In ΔABD and ΔPQS

<B = <Q (ΔABC ~ ΔPQR)

<ADB = <PSO (Each 90°)

Then , ΔABD ~ ΔPQS (By AA similarity)

So, AB/ PQ = AD/PS

6/5 = AD/ PS (From iv)