A parallelogram is divided into 20 regions of equal area by drawing line segment

Question

A parallelogram is divided into 20 regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the longest line segment to one the shortest one?

Options:

A . 3:2

B . 4:3

C . 3:1

D . 5:2

Answer: Option C
:
C

A Parallelogram Is Divided Into 20 Regions Of Equal Area By ...

The figure looks as above.

Δ

ABE and

Δ

CDE are similar.
The area of each part is equal.
Thus the ratios of the areas= square of the ratios of the corresponding sides

\Rightarrow

If area of ∆CDE = x then area of

Δ

ABE =9x

∴

\frac{C D}{A B} = \sqrt{\frac{9 x}{x}}

= 3:1

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