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.

2 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $1 m$
Let the width of the path be $x$ .

The length and width of the outer rectangle is
$L e n g t h = 20 + 2 x$

$W i d t h = 14 + 2 x$

The area of the outer rectangle is
$(14 + 2 x) (20 + 2 x) = 4 x^{2} + 68 x + 280$

The area of the field
$14 \times 20 = 280 m^{2}$

The area of the path is the difference between the two areas :
$(4 x^{2} + 68 x + 280) - 280 = 4 x^{2} + 68 x$

$4 x^{2} + 68 x = 72$

$4 x^{2} + 68 x - 72 = 0$

$x^{2} + 17 x - 18 = 0$

$x^{2} + 18 x - x - 18 = 0$

$x (x + 18) - 1 (x + 18) = 0$

$x = 1, - 18$

$x$ can not be $- v e$

So, $x = 1$

Width of the path is $1 m$ .

Hence, this is the answer.

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

111 s q m

. Find the width of the path.

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.

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

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

30 m

long and

24 m

wide. If the path occupies

360 m^{2}

, find its width.

Q. A footpath of uniform width runs around the outside of a rectangular field 20 m long and 10 m wide. If the path occupies

136 m^{2},

its width is .

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 72 m2. Find the width of the path on the outside.

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.