Question

If the ratio of the corresponding sides of two similar triangles is 2 ratio 3 then find the ratio of its corresponding height

Answer 1

let triangle ABC is similar to triangle PQR and AB/PQ = 2/3  ....(1)

and draw the heights AD and PM.

Now, In triangle ABD and triangle PQR

  <B = < Q  (since ABC similar PQR )

  <ADB = < PMQ (each 900 )   so, triangle ABD similar to triangle PQM ( by AA similarity )

  so, AD/PM = AB/PQ

  or  (AD/PM)2 =  (AB/PQ)2..............(2)

  since triangle ABC similar to triangle PQR

therefore  ar.(ABC)/ar(PQR) = (AB/PQ)2

  =  ( AD/PM )2 (using 2 )

  = (2/3)2 = 4/9 = 4:9

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