Question

It is given that ΔАBC ~ ΔDFE, ∠A = 30°, ∠C = 50°, AB = 5cm, AC = 8 cm and DF = 7.5 cm. Then DE = ______ and F = ______.

Answer 1

It is given that ΔАBC ~ ΔDFE, ∠A = 30°, ∠C = 50°, AB = 5cm, AC = 8 cm and DF = 7.5 cm. Then DE = 12 cm and F = 100°.

Explanation:

From ΔABC ~ ΔDFE the correspondence is A↔D, B↔F, C↔E, so AB ↔ DF and AC ↔ DE. By similarity corresponding sides are proportional.

Scale factor `k = (DF)/(AB)`

= `7.5/5`

= 1.5 

So DE = k × AC

= 1.5 × 8

= 12 cm

Angles correspond likewise, so ∠F = ∠B.

Since ∠A = 30° and ∠C = 50°

∠B = 180° – 30° – 50° = 100°

Hence ∠F = 100°.