Q. 64.2( 5 Votes )

The areas of two

Answer :

We have,

ΔABC ~ Δ PQR


Area (ΔABC) = 25 cm2


Area (PQR) = 36 cm2


And AD = 2.4 cm


And AD and PS are the altitudes


To find: PS


Proof: Since, ΔABC ~ ΔPQR


Then, by area of similar triangle theorem


Area of ΔABC/Area of ΔPQR = AB2 /PQ2


25/36 = AB2/PQ2


5/6 = AB/PQ………………..(i)


In ΔABD and Δ PQS


<B = <Q (ΔABC ~ ΔPQR)


<ADB = <PSQ (Each 90°)


Then, ΔABD ~ Δ PQS (By AA similarity)


So, AB/PS = AD/PS…………(ii) (Corresponding parts of similar Δ are proportional )


Compare (i) and (ii)


AD/PS = 5/6


2.4/PS = 5/6


PS = 2.4 x 6/5


PS = 2.88cm


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