# GMAT Math Questions | Geometry #12

#### Length of the diagonal of a square | Rates | Speed Distance Time

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?

1. 3 minutes
2. 0.04 hours
3. 2 minutes
4. 2.4 minutes
5. 2 minutes 40 seconds

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### Explanatory Answer | GMAT Geometry

#### Step 1 to solving this GMAT Geometry Question: 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 = √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{2 \times area}$ meters. d = $\sqrt{2 \times 24200}$ = $\sqrt{48400}$ = 220 m. #### Step 2 to solving this GMAT Geometry Question: 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 = $\frac{\text{6.6 × 1000}}{\text{60}}$ m/min = 110 m/min ∴ time taken = $\frac{\text{220 m}}{\text{110 m/min}}$ = 2 minutes #### Choice C is the correct answer. #### GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GMAT Live Online Classes Next Batch Sep 21, 2023 ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 95000 48484
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