AD and BC are two poles, that are respectively 30 metres and 15 metres tall, and both stand upright in a playground, A and B, respectively the feet of the two poles AD and BC, are 36 metres apart and \(\overline{CE}\) | \(\overline{BA}\), intersecting \(\overline{AD}\) at E. Find the ratio of the area of ΔDEC to the area of the rectangle ABCE.

Question

Question

This question was previously asked in

RRB Group D 26 Sept 2022 Shift 2 Official Paper

Answer 1

Given:

AD = 30 m

BC = 15 m

AB = 36 m

Formula used:

Area of rectangle = length x breadth

Area of triangle = \(\frac{1}{2}\)(base x height)

Calculation:

recta.drawio

In Rectangle ABCE,

Length = AB = 36m

Breadth = BC = 15m

Area of rectangle = l x b

= 36 x 15

= 540 m²

In Triangle ΔDEC,

Height = ED = AD - AE

AE = BC = 15 m

ED = 30 - 15 = 15 m

Height = 15 m

Base = CE = AB = 36 m

Area of triangle = \(\frac{1}{2}\) x 36 x 15

= 270 m²

Now, the ratio of the area of ΔDEC to the area of the rectangle ABCE

= 270 : 540

= 1 : 2

Hence, the correct answer is '1 : 2'.

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