Question

UL
25. 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 an area
of 360 m2, find its width.​

Answer 1

Given:-

• Length of rectangular field = 30m.
• Breadth of rectangular field = 24m.
• The path occupies an area of 360m².

To find:-

• The width of the path.

Solution:-

Let width of the path be x.

Then ,

→ length of rectangular field and path = 2x + 30

→ Breadth = 2x + 24

→ Area of rectangular field = (l × b).

⇒ Area = 30 × 24 = 720

Now,

→ Area of rectangular field and path = (2x+30)(2x+24)

According to question ,

⇒ (2x+24)(2x+30)-720 = 360

⇒ 4x²+48x+60x +720 - 720 =360

⇒4x² +27x-90=0

⇒x²+30x-3x-90=0

⇒ x(x+30)-3(x+30)=0

⇒ (x+30)(x-3)=0

⇒ x = -30  or x=3.

Negative value cannot be taken .

∴ $\sf { \boxed{ Width = 3cm.}}$

_______________________________

Answer 2

Given:-

Length of rectangular field = 30m.

Breadth of rectangular field = 24m.

The path occupies an area of 360m².

To find:-

The width of the path.

Solution:-

Let width of the path be x.

Then ,

→ length of rectangular field and path = 2x + 30

→ Breadth = 2x + 24

→ Area of rectangular field = (l × b).

⇒ Area = 30 × 24 = 720

Now,

→ Area of rectangular field and path = (2x+30)(2x+24)

According to question ,

⇒ (2x+24)(2x+30)-720 = 360

⇒ 4x²+48x+60x +720 - 720 =360

⇒4x² +27x-90=0

⇒x²+30x-3x-90=0

⇒ x(x+30)-3(x+30)=0

⇒ (x+30)(x-3)=0

⇒ x = -30  or x=3.

Negative value cannot be taken .

∴ $\sf { \boxed{ Width = 3cm.}}$

_______________________________