A footpath of uniform width runs around the inside of a rectangular field 12 m long and 14 m wide. If the path occupies $56 m^{2}$ , the second degree equation from which we can find the width of the path is ______.(Take width = x)

$3 x^{2} - 52 x + 56 = 0$

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

$4 x^{2} - 52 x + 58 = 0$

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

$4 x^{2} - 54 x + 56 = 0$

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

$4 x^{2} - 52 x + 56 = 0$

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

Open in App

Solution

The correct option is D
$4 x^{2} - 52 x + 56 = 0$

Area of outer rectangle $= 12 \times 14 m^{2} = 168 m^{2}$

Width of the footpath= $x$ m

Area of inner rectangle $= (12 - 2 x) (14 - 2 x) m^{2} = 4 x^{2} - 52 x + 168 m^{2}$

Area of footpath = Area of outer rectangle - Area of inner rectangle

$\Rightarrow 56 = 168 - (4 x^{2} - 52 x + 168)$

$\Rightarrow 56 = 168 - 4 x^{2} + 52 x - 168$

$\Rightarrow 56 = - 4 x^{2} + 52 x$

$\Rightarrow 4 x^{2} - 52 x + 56 = 0$

Suggest Corrections

Similar questions

A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 $m^{2}$ , find the width of the footpath.

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 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.

A footpath of uniform width runs all around the inside of a rectangular field 28 m long and 22 m wide. If the path occupies 600 $m^{2}$ , what is the width of the path?

Join BYJU'S Learning Program

A footpath of uniform width runs around the inside of a rectangular field 12 m long and 14 m wide. If the path occupies 56 m2, the second degree equation from which we can find the width of the path is ______.(Take width = x)

A footpath of uniform width runs around the inside of a rectangular field 12 m long and 14 m wide. If the path occupies $56 m^{2}$ , the second degree equation from which we can find the width of the path is ______.(Take width = x)