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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?
- a)3 minutes
- b)2 minutes
- c)2.4 minutes
- d)2 minutes 40 seconds
- e)3.4 minutes
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The area of a square field is 24200 sq m. How long will a lady take to...
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 =
a –-- (2)
From (1) and (2), we can deduce that the square of the diagonal = d2 = 2a2
Or d =
meters.
Therefore, its area = a2 square meters. --- (1)
We know that the length of the diagonal ‘d’ of a square whose side is ‘a’ meters =
a –-- (2)From (1) and (2), we can deduce that the square of the diagonal = d2 = 2a2
Or d =
meters.The time taken to cross a length of 220 meters while traveling at 6.6 kmph is given by
(converting 1 km = 1000 meters and 1 hour = 60 minutes).= 2 minutes
(converting 1 km = 1000 meters and 1 hour = 60 minutes).= 2 minutesMost Upvoted Answer
The area of a square field is 24200 sq m. How long will a lady take to...
Solution:
Given, Area of square field = 24200 sq m
Let each side of the square be 'a'.
Area of square = a^2
Therefore, a^2 = 24200 sq m
a = √24200 = 2√6050 m
Length of diagonal of square = √2 times of its side
= √2 × 2√6050
= 2 × √2 × √6050
= 2 × √(2 × 6050)
= 2 × √(2 × 2 × 5 × 11 × 55)
= 2 × 22 × √(5/2)
= 44 × √10 m
Distance to be covered by the lady = length of diagonal = 44 × √10 m
Now, speed of the lady = 6.6 km/hr
= 6.6 × 1000 m / 60 minutes
= 110 m / minute
Time taken by the lady to cross the field diagonally
= Distance / Speed
= (44 × √10) / 110
= 4 / √10 minutes
= 4 / √10 × (√10 / √10)
= 4√10 / 10
= 2√10 / 5 minutes
= 2 × √10 / 5 × (60 seconds)
= 2 × 12 / 5 seconds
= 24 / 5 seconds
= 4.8 seconds
= 5 seconds (approx)
Therefore, the lady will take 2 minutes (approx) to cross the field diagonally. Hence, option B is the correct answer.
Given, Area of square field = 24200 sq m
Let each side of the square be 'a'.
Area of square = a^2
Therefore, a^2 = 24200 sq m
a = √24200 = 2√6050 m
Length of diagonal of square = √2 times of its side
= √2 × 2√6050
= 2 × √2 × √6050
= 2 × √(2 × 6050)
= 2 × √(2 × 2 × 5 × 11 × 55)
= 2 × 22 × √(5/2)
= 44 × √10 m
Distance to be covered by the lady = length of diagonal = 44 × √10 m
Now, speed of the lady = 6.6 km/hr
= 6.6 × 1000 m / 60 minutes
= 110 m / minute
Time taken by the lady to cross the field diagonally
= Distance / Speed
= (44 × √10) / 110
= 4 / √10 minutes
= 4 / √10 × (√10 / √10)
= 4√10 / 10
= 2√10 / 5 minutes
= 2 × √10 / 5 × (60 seconds)
= 2 × 12 / 5 seconds
= 24 / 5 seconds
= 4.8 seconds
= 5 seconds (approx)
Therefore, the lady will take 2 minutes (approx) to cross the field diagonally. Hence, option B is the correct answer.
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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?a)3 minutesb)2 minutesc)2.4 minutesd)2 minutes 40 secondse)3.4 minutesCorrect answer is option 'B'. Can you explain this answer?
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