Question

If ΔABC ~ ΔDEF and ar(ΔABC) : ar(ΔDEF) = 25 : 4, then BC : EF is ______.

पर्याय

• 3 : 2

• 2 : 3

• 5 : 2

• 2 : 5

Answer 1

If ΔABC ~ ΔDEF and ar(ΔABC) : ar(ΔDEF) = 25 : 4, then BC : EF is 5 : 2.

Explanation:

Since △ABC ∼ △DEF, the ratio of their areas is equal to the square of the ratio of their corresponding sides:

`"ar(ΔABC)"/"ar(ΔDEF)" = ((BC)/(EF))^2`

Given,

`"ar(ΔABC)"/"ar(ΔDEF)" = 25/4`

So,

`((BC)/(EF))^2 = 25/4`

`(BC)/(EF) = sqrt(25/4)`

`(BC)/(EF) = 5/2`

∴ BC : EF = 5 : 2