Question

In ΔABC, it is given that AB = 9 cm, BC = 6 cm and CA = 7.5 cm. Also, ΔDEF is given such that EF = 8 cm and ΔDEF ~ ΔABC. Then, perimeter of ΔDEF is ______.

पर्याय

• 22.5 cm

• 25 cm

• 27 cm

• 30 cm

Answer 1

In ΔABC, it is given that AB = 9 cm, BC = 6 cm and CA = 7.5 cm. Also, ΔDEF is given such that EF = 8 cm and ΔDEF ~ ΔABC. Then, perimeter of ΔDEF is 30 cm.

Explanation:

Because ΔDEF ~ ΔABC the vertex order gives D ↔ A, E ↔ B, F ↔ C, so EF corresponds to BC and corresponding sides are in the same ratio.

Thus, scale factor `k = (EF)/(BC)`

= `8/6`

= `4/3` 

Perimeter of ABC = 9 + 6 + 7.5

= 22.5 cm 

Perimeter of DEF = k × 22.5

= `4/3 xx 22.5`

= 30 cm