If `DeltaABC~DeltaDFE,angleA=30,angleC=50^(@)`,AB=5 cm,AC=8 cm and DF= – InterviewSolution

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1.	If `DeltaABC~DeltaDFE,angleA=30,angleC=50^(@)`,AB=5 cm,AC=8 cm and DF=7.5 cm. Then, which of the following is true?A. `DE=12 cm, angle F=50^(@)`B. `DE=12 cm, angle F=100^(@)`C. `EF=12 cm, angle D=100^(@)`D. `EF=12 cm, angle D=30^(@)`
Answer» Correct Answer - B `angle B=180^(@)-(30^(@)+50^(@))=100^(@)` Since `Delta ABC~Delta DEF`, we have `angle D= angleA=30^(@), angle F= angle B=100^(@) and angle E= angle C=50^(@)`. Let the `DE=x` cm. then, `(AB)/(DF)=(AC)/(DE)rArr (5)/(7.5)=(8)/(x)` `:. 5x=8xx7.5 rArr x(8xx7.5)/(5) =12` Hence, `DE=12 cm and angle F=100^(@)`

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