Q22

Q22 - Let ABCD be a rectangle and let E and F be points on CD and BC respectively such that area (ADE) = 16, area (CEF) = 9 and area (ABF) = 25. What is the area of triangle AEF?

Answer: 30
Solution:
Let a,b be the sides of rectangle.
Once you set up all the area equations for the triangle areas given, and remove all the variables except a,b, you will get a quadratic in (ab).
Upon solving you will get ab = 80,20.
ab = 20 not possible as the area of rectangle can't be less than the triangles inside it.
So ab = 80.
Area of the remaining triangle = 80 - (16+9+25) = 30.

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