Q. 54.4( 9 Votes )

Two isosceles tri

Answer :

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)


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