Question

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

Answer 1

Answer:

Step-by-step explanation:

Solution :-

Let the width of the path be x m.

Then, the length of the path be 20 + 2x m.

And the width of the path be 14 + 2x m.

According to the Question,

Area of rectangular path = Length × Breadth

= (20 + 2x) (14 + 2x)

= 4x² + 68x + 280  

Area of the path = 111 m²

⇒ 4x² + 68x + 280  = 111 m²

Subtracting 280 from left side,

⇒ 4x² + 68x + 280 - 280  = 111 m²

⇒ 4x² + 68x = 111 m²

⇒ 4x² + 68x - 111 = 0

⇒ 4x² + 74x - 6x - 111 = 0

⇒ 2x(2x + 37) - 3(2x + 37) = 0

⇒ (2x + 37) (2x - 3) = 0

⇒ x = - 37/2, 3/2 = 0

⇒ x = - 18.5, 1.5 (As x can't be negative)

⇒ x = 1.5 m

Hence, the width of the path is 1.5 m.

Answer 2

ANSWER:

Given

• Length of rectangular field = 20m
• Width of rectangular field = 14m
• Area of path = 111 m²
• Let the width of the path be 'x'
• Then the length of path will be 20 + 2x
• And width will be 14 + 2x

Area of rectangular path = length × Breadth

→ 111m² = (20 + 2x) (14 + 2x)

→ 111m² = 280 + 40x + 28x + 4x²

→ 111m² = 4x² + 68x + 280

Subtracting 280 on LHS

→ 4x² + 68x + 280 - 280 = 111

→ 4x² + 68x - 111 = 0

Now , we get a quadratic equation

Solving using factorisation

Splitting the middle term

→ 4x² + 74x - 6x - 111 = 0

→ 2x(2x + 37) - 3(2x + 34) = 0

→ (2x + 37)(2x - 3) = 0

2x + 37 = 9

x = -37/2 = - 18.5

_________________

2x - 3 = 0

x = 3/2 = 1.5

x = - 18.5 , 1.5

Hence distance can't be negative

♦ x = 1.5

Hence, width of the path = 1.5m