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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?
Options
DE = 12 cm, ∠F = 50°
DE = 12 cm, ∠F = 100°
EF = 12 cm, ∠D = 100°
EF = 12 cm, ∠D = 30°
MCQ
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Solution
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°.
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