This GMAT quant problem solving practice question is from Mensuration (Solid Geometry): Concept: Length of the diagonal of a square and elementary speed, distance, and time concepts. A medium difficulty GMAT 650 level question.
Question 12: 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?
Let 'a' meters be the length of a side of the square field.
Therefore, its area = a2 square meters. --- (1)
The length of the diagonal 'd' of a square whose side is 'a' meters = √2 a --- (2)
From (1) and (2), we can deduce that the square of the diagonal = d2 = 2a2 = 2(area of the square)
Or d = √2×area meters.
d = √2×24200 = √48400 = 220 m.
The time taken to cross a distance of 220 meters while traveling at 6.6 kmph = 220 m6.6 kmph
1 km = 1000 meters and 1 hour = 60 minutes.
So, 6.6 kmph = 6.6 × 100060 m/min = 110 m/min
∴ time taken = 220 m110 m/min = 2 minutes
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