Question

(iii) If ∆ABC ~ ∆DEF, A (∆ABC) = 36 cm2, A (∆DEF) = 64 cm2, what is the
ratio of the length of sides BC and EF

Answer 1

Ratio BC and EF = 3 : 4

BC = 6 cm

EF = 8 cm

Step-by-step explanation:

Q.

If ∆ABC ~ ∆DEF, Ar(∆ABC) = 36 cm², Ar(∆DEF) = 64 cm². What is the ratio of Length of sides BC and EF

Solution -

We know that,

When Two triangles are similar, then ratio of their area = (ratio of their corresponding sides)²

=> Ar(∆ABC) / Ar(∆DEF) = (AB/DE)² = (BC/EF)² = (AC/DF)²

=> Ar(∆ABC) / Ar(∆DEF) = (BC/EF)²

=> 36 cm²/64 cm² = (BC/EF)²

=> √(36 cm²/64 cm²) = √(BC/EF)²

=> 6 cm / 8 cm = BC/EF

Hence,

ratio of BC and EF = 6 : 8 = 3 : 4.

hope it helps.