A rectangular field is $20 m$ long and $14 m$ wide. There is a path of equal width all around it, having an area of $111 s q m$ . Find the width of the path.

Open in App

Solution

Let width of path $x$
Length $= 20 + 2 x$
Width $= 14 + 2 x$

Area of outer rectangular $= l \times b$
$\begin{matrix} = (20 + 2 x) (14 + 2 x) = 4 x^{2} + 68 x + 280 \end{matrix}$

Area of path:
$4 x^{2} + 68 x + 280 - 280 = 111 4 x^{2} + 68 x = 111 4 x^{2} + 68 x - 111 = 0 (4 x^{2} + 74 x - 6 x - 111) = 0$
$(2 x - 3) (2 x + 37) = 0$
$x = \frac{3}{2} m$ or $x = - \frac{37}{2}$

Since, width can not be $- v e$

Hence, the width is $1.5 m$ .

Suggest Corrections

Similar questions

Q. A rectangular field is

20 m

long and

14 m

wide.There is a path of equal width all around it having an area of

72 m^{2}

. Find the width of the path on the outside.

A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 $m^{2}$ . Find the width of the path.

A foot path of uniform width runs all around inside of a rectangular field 45m long and 36m wide. If the area of the path is 234m^2,find the width of the path

Q. A footpath of uniform width runs all around the inside of a rectangular field 54 m long and 35 m wide. If the area of the path is 420 m²., find the width of the path.

Q. A footpath of uniform width runs all around the outside of a rectangular field

30 m

long and

24 m

wide. If the path occupies

360 m^{2}

, find its width

Join BYJU'S Learning Program

A rectangular field is 20 m long and 14 m wide. There is a path of equal width all around it, having an area of 111 sq m. Find the width of the path.

Let width of path xLength =20+2xWidth =14+2xArea of outer rectangular =l×b=(20+2x)(14+2x)=4x2+68x+280Area of path:4x2+68x+280−280=1114x2+68x=1114x2+68x−111=0(4x2+74x−6x−111)=0(2x−3)(2x+37)=0x=32 m or x=−372Since, width can not be −veHence, the width is 1.5 m.

A rectangular field is $20 m$ long and $14 m$ wide. There is a path of equal width all around it, having an area of $111 s q m$ . Find the width of the path.