# GMAT Quant Practice: Solid Geometry

Concept: Length of the diagonal of a square. Basic rates concepts.

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.

#### Question: 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. 0.04 hours
3. 2 minutes
4. 2.4 minutes
5. 2 minutes 40 seconds

Video explanation will be added soon

#### Compute the length of the diagonal of the square

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 = $$sqrt{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 = $\sqrt{\text{2 * area}}\\$ meters.

d = $\sqrt{2 * 24200} = \sqrt{48400}\\$ = 220 m.

#### Compute the time taken to cross the field

The time taken to cross a distance of 220 meters while traveling at 6.6 kmph = $\frac{\text{220 m}}{\text{6.6 kmph}}\\$

##### Convert unit of speed from kmph to m/min

1 km = 1000 meters and 1 hour = 60 minutes. So, 6.6 kmph = $\frac{6.6 * 1000}{60 }\\$ m/min = 110 m/min

∴ time taken = $\frac{220}{110}\\$ = 2 minutes

Choice C is the correct answer.

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