A cow is tied with a rope of length \[14\] m at the corner of a rectangular field of dimensions \[20m\times 16m\]. Find the area of the field in which the cow can graze.

Home » A cow is tied with a rope of length m at the corner of a rectangular field of dimensions . Find the area of the field in which the cow can graze.

A cow is tied with a rope of length

$14$

m at the corner of a rectangular field of dimensions

$20m\times 16m$

. Find the area of the field in which the cow can graze.

A cow is tied with a rope of length

$14$

m at the corner of a rectangular field of dimensions

$20m\times 16m$

. Find the area of the field in which the cow can graze.

Let us consider ABCD be a rectangular field.

Given, Length of the field =

$20$

m

Given, Breadth of the field =

$16$

m

From the given question,

A cow is tied with a rope at a point A.

Let us consider length of rope be AE =

$14$

m = l.

We know that Angle subtended at the centre of the sector =

${{90}^{\circ }}$

Now for Angle subtended at the center (in radians)

$\theta$

=

$90\pi /180$

=

$\pi /2$

∴ Area of a sector of a circle =

$\frac{1}{2}{{r}^{2}}\theta$

=

$\frac{1}{2}\times {{(14)}^{2}}\times (\pi /2)$

=

$154$

${{m}^{2}}$

Therefore, the area of the field in which cow can graze is

$154$

${{m}^{2}}$

i

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