Question

A foot path of uniform width runs all around outside of a rectangular field 30 M long and 24 why did the part occupies an area of 360 metre square find its width

Answer 1

Answer:

• The width of the path = 3 m

Given :

• The length of the rectangular field = 30 m.

• The width of the rectangular field = 24 m.

• The Area of the rectangular field = 360 m².

To find :

• The width of the path =?

Step-by-step explanation:

Let the width of the path be x.

Then, the length of the rectangular field and path =2x+30

So, breadth =2x+24

And, Area of rectangular field =(30×24)

=720

Therefore, Area of the rectangular field and path =(2x+30)(2x+24)

Now,

According to the question :

(2x+30) (2x+24)−720 = 360

⇒4x 2 +48x+60x+720−720=360

⇒4x 2 +108x−360=0

⇒x 2 +27x−90=0

⇒x 2 +30x−3x−90=0

⇒x(x+30)−3(x+30)=0

⇒(x+30)(x−3)=0

⇒x=−30 and x=3

Negative value is not valid,

So, We have to take positive value = 3.

Thus, the width of the path = 3 m