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Home » It is given that ∆ABC~∆DFE. If ∠A = , ∠C = , , AB = 5cm, AC = 8cm and DF = 7.5cm, then which of the following is true? (a) DE = 12cm, ∠F = , (b) DE = 12cm, ∠F = , (c) DE = 12cm, ∠D = , (d) EF = 12cm, ∠D = ,
It is given that ∆ABC~∆DFE. If ∠A = {30^0}, ∠C = {50^0}, , AB = 5cm, AC = 8cm and DF = 7.5cm, then which of the following is true? (a) DE = 12cm, ∠F = {50^0}, (b) DE = 12cm, ∠F = {100^0}, (c) DE = 12cm, ∠D = {100^0}, (d) EF = 12cm, ∠D = {30^0},
CBSE | Class 10 | Exercise MCQ | Maths | RS Aggarwal | Triangles
It is given that ∆ABC~∆DFE. If ∠A = {30^0}, ∠C = {50^0}, , AB = 5cm, AC = 8cm and DF = 7.5cm, then which of the following is true? (a) DE = 12cm, ∠F = {50^0}, (b) DE = 12cm, ∠F = {100^0}, (c) DE = 12cm, ∠D = {100^0}, (d) EF = 12cm, ∠D = {30^0},

Correct Answer: (b) DE = 12cm, ∠F = {100^0}

Explanation:

Given,

In triangle ABC,

∠???? + ∠???? + ∠???? = 1800

∠???? = 180 − 30 − 50 => 1000

∵ ∆ABC ~ ∆DFE

∠???? = ∠???? = 300

∠???? = ∠???? = 1000

∠???? = ∠???? = 500

\begin{array}{l} \frac{{AB}}{{DF}} = \frac{{AC}}{{DE}}\\ \frac{{5}}{{7.5}} = \frac{{B}}{{DE}}\\ DE = \frac{{8 \times 7.5}}{{5}}\\ DE = 12cm \end{array}

i

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