Question

It is given that ΔABC ~ ΔDFE, ∠A =30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true ______.

Options

• DE = 12 cm, ∠F = 50°

• DE = 12 cm, ∠F = 100°

• EF = 12 cm, ∠D = 100°

• EF = 12 cm, ∠D = 30°

Answer 1

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

Explanation:

Given, ∆ABC ~ ∆DFE,

Then ∠A = ∠D = 30°,

∠C = ∠E = 50°

∴ ∠B = ∠F = 180° – (30° + 50°) = 100°

Also, AB = 5 cm,

AC = 8 cm

And DF = 7.5 cm

∴ `("AB")/("DF") = ("AC")/("DE")`

`\implies 5/7.5 = 8/("DE")`

∴ DE = `(8 xx 7.5)/5` = 12 cm

Hence, DE = 12 cm, ∠F = 100°