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प्रश्न
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 ______.
विकल्प
DE = 12 cm, ∠F = 50°
DE = 12 cm, ∠F = 100°
EF = 12 cm, ∠D = 100°
EF = 12 cm, ∠D = 30°
उत्तर
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°
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