The area of a rectangular field is $48\ m^2$ and one of its sides is $6\ m$. How long will a lady take to cross the field diagonally at the rate of $20$ m/minute?
Given:
The area of a rectangular field is $48\ m^2$ and one of its sides is $6\ m$.
To do:
We have to find the time it takes to cross the field diagonally at the rate of $20$ m/minute.
Solution:
We know that,
Area of a rectangle of length $l$ and breadth $b$ is $lb$.
Let the other side of the rectangle be $x$.
This implies,
$48=6\times x$
$x=\frac{48}{6}$
$x=8\ m$
Length of the diagonal $=\sqrt{6^2+8^2}$
$=\sqrt{36+64}$
$=\sqrt{100}$
$=\sqrt{(10)^2}$
$=10\ m$
Time taken by the lady to cross the field diagonally at the rate of $20$ m/minute $=\frac{Length\ of\ the\ diagonal}{Rate}$
$=\frac{10}{20}$ minutes
$=\frac{1}{2}$ minute
$=\frac{1}{2}\times60$ seconds
$=30$ seconds
Therefore, the time taken by the lady to cross the field diagonally at the rate of $20$ m/minute is 30 seconds.
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