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In ΔABC, a line through A cuts the side BC at D such that BD : DC = 4 : 5. If the area of ΔABD = 60 cm2, then the area of ΔADC is    (SSC CGL 1st Sit. 2015)
  • a)
    50 cm2
  • b)
    60 cm2
  • c)
    75 cm2
  • d)
    90 cm2
Correct answer is option 'C'. Can you explain this answer?
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In ΔABC, a line through A cuts the side BC at D such that BD : D...

Let AE is the height of the triangle ABC, then

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In ΔABC, a line through A cuts the side BC at D such that BD : D...

Let AE is the height of the triangle ABC, then

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In ΔABC, a line through A cuts the side BC at D such that BD : D...
Given information:
- In ΔABC, a line through A cuts the side BC at D such that BD : DC = 4 : 5.
- Area of ΔABD = 60 cm2

Calculating the area of ΔADC:
- Let the area of ΔADC be x cm2.
- Since BD : DC = 4 : 5, let the length of BD be 4k and DC be 5k.
- The area of a triangle is proportional to the product of its base and height.
- Therefore, the area of ΔABD : Area of ΔADC = BD : DC (since they share the same height)
- 60 : x = 4 : 5
- 60/4 = x/5
- x = 75 cm2
Therefore, the area of ΔADC is 75 cm2, which is option 'c'.
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In ΔABC, a line through A cuts the side BC at D such that BD : DC = 4 : 5. If the area of ΔABD = 60 cm2, then the area of ΔADC is (SSC CGL 1st Sit. 2015)a)50 cm2b)60 cm2c)75 cm2d)90 cm2Correct answer is option 'C'. Can you explain this answer?
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