Mensuration Questions Answers

Quant/Math - CAT 2008

Question 4 the day: Mensuration - March 22, 2004

The question for the day is from the topic Mensuration.

The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?

(1)	3 minutes			(2)	2 minutes
(3)	2.4 minutes			(4)	2 minutes 40 seconds

Correct choice - (2) Correct Answer -(2 minutes)

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Solution:

Let �a� meters be the length of a side of the square field.

Therefore, its area = a² square meters. --- (1)

We know that the length of the diagonal �d� of a square whose side is �a� meters = 2^1/2 a �-- (2)

From (1) and (2), we can deduce that the square of the diagonal = d² = 2a²

Or d =   (2*area)^1/2 = (2*24300)^1/2 =  48400^1/2  =220meters.

The time taken to cross a length of 220 meters while traveling at 6.6 kmph is given by
 220 meters  /  6.6kmph  =  220*60  /  6.6*1000(converting 1 km = 1000 meters and 1 hour = 60 minutes).

= 2 minutes