Question

A man walking at the rate of 6km per hour crosses a square field diagonally in 9

seconds. The area of the field is​

Answer 1

Answer:

113 m sq.

Step-by-step explanation:

Speed of man=6km/h=6×5/18 m per s

=1.67m/s

Distancs travelled in 9s =9×1.67=15.03m

Length of diagonal=15.03m

By pythagoras theorem,

x^2+x^2=15.03× 15.03 , where x is the side of square

2x^2=226

x^2=113

Hence area of square is 113 m sq. (approx.)

Answer 2

Area of the field is 112.5 square meters.

Step-by-step explanation:

The speed of the man is 6 km/hr.

Convert this speed in m/s

$6 km/hr = 6\cdot\frac{5}{18}\\\\=\frac{5}{3}m/s$

Now, he crosses the diagonal in 9 seconds.

Thus, length of the diagonal is given by

$d=vt\\\\d=\frac{5}{3}\cdot9\\\\d=15m$

Area of the square is given by

$A=\frac{1}{2}d^2\\\\A=\frac{1}{2}(15)^2\\\\A=\frac{225}{2}\\\\A=112.5\text{ sq.m}$

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