CAT 1994 — QA Question 32
Data is provided followed by two statements – I and II – both resulting in a value, say I and II.
As your answer,
Type 1, if I > II.
Type 2, if I < II.
Type 3, if I = II.
Type 4, if nothing can be said.
In ΔACD, AD = AC and ∠C = 2∠E. The distance between parallel lines AB and CD is h. Then
I. Area of parallelogram ABCD
II. Area of ΔADE
Answer & solution
Correct answer: 3
Answer: 3
Since ∠C = 2 ∠E , therefore ∠BCA = 60°.
Also since ABCD is a parallelogram,
AB = CD and AD = BC = AC.
Hence, ΔABC and ΔACD are equilateral triangles.
Hence, area of this triangle =
where s is the side of the triangle = AB = AD = DC = BC.
∴ Area of the parallelogram is twice this area =
Since ∠CAD = 60°, ∠DAE = 90°, so ΔEAD is a right triangle with side AD = s. Since it is a 30-60-90 triangle, hence side AE = s
∴ Area of this triangle =
Hence, the required two areas are equal or I = II.