. Let ABCD be a rectangle and E and F be the points on CD and BC respectively such that area of (Δ ADE) = 16, area (ΔCEF) = 9 and area (ΔABF) = 25. What


A. 28
B. 30
C. 32
D. 36

 

Best Answer

Answer : ||| D

Solution : |||

 

 ABCD be a rectangle and E and F be the points on CD and BC respectively such that area of (Δ ADE) = 16, area (ΔCEF) = 9 and area (ΔABF) = 25

To find – Area of ΔAEF

Areas related to ciccle

Let AD = a units

In ∆ADE,

½ x DE x a = 16

⇨ DE = 32/a

Let AB = b units

In ∆ABF,

½ x b x BF = 25

⇨ BF = 50/b

In ∆CEF,

½ x CE x CF = 9

⇨(b – 32/a)(a – 50/b) = 18

⇨(ab – 32)(ab – 50) = 18ab

⇨(ab)2 – 100ab + 1600 = 0

⇨(ab – 20)(ab – 80) = 0

If ab = 20,

ab = ∆ADE + ∆ABF + ∆CEF + ∆AEF >16 + 9 +25

which cannot be the case

So,

ab = 80 since ab = 20 would be absurd

Area of ∆AEF

= rectangle ABCD - ∆ADE - ∆CEF - ∆ABF

= ab – 16 – 9 – 25

= 80 – 50

= 30 sq units

Hence, the correct answer is D


 

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