Question

Question 62

The area of a rectangular field is $48m^2$ and one of its sides is 6m. How long will a lady take to cross the field diagonally at the rate of 20 m/min?

Answer 1

Given, the area of a rectangular field is $48m^2$ and one side of the rectangle is = 6 m.

$\therefore$ Area of a rectangle $=Length\times Breadth$
$\Rightarrow 48=6\times Breadth$
$\Rightarrow$ Breadth= 8m
In $\Delta ACD,\angle D={90}^{\circ }$ [$\because$ in a rectangle , all angles are of ${90}^{\circ }$]
So, it is a right-angled triangle
By using Pythagoras theorem, we have
$(AC{)}^2=(AD{)}^2+(DC{)}^2\Rightarrow (AC{)}^2=(6{)}^2+(8{)}^2\Rightarrow (AC{)}^2=36+64\Rightarrow AC=\sqrt{100}\therefore AC=10m$
Time taken by lady to cross the field diagonally at rate 20 m/min $=\frac{Distance}{Speed}$
$=\frac{10}{20}=\frac{1}{2}min$ or 30 s