Question

It is given that ΔАBС ~ ΔDFE. If ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm then which of the following is true?

विकल्प

• DE = 12 cm, ∠F = 50°

• DE = 12 cm, ∠F = 100°

• EF = 12 cm, ∠D = 100°

• EF = 12 cm, ∠D = 30°

Answer 1

DE = 12 cm, ∠F = 100°

Explanation:

From ΔABC ~ ΔDFE the correspondence is AD, BF, CE.

So, ∠F = ∠B

= 180° – 30° – 50°

= 100° 

By similarity, corresponding sides are proportional.

Use `(AC)/(DE) = (AB)/(DF)`

⇒ `DE = (AC xx DF)/(AB)`

= `(8 xx 7.5)/5`

= 12 cm

Thus, DE = 12 cm and ∠F = 100°.