Question

al -00
0
.
| Length of a rectangular field is 20 m and breadth is 15 m. Apath of equal breadth is
out side the field whose area is 156 sq. m. Find the breadth of path.
एक आयताकार मैदान 20 मी लम्बा और 15 मी चौड़ा है। इसके चारो और एक समान चौड़ाई
का रास्ता है। जिसका क्षेत्रफल 156 वर्ग मी है। रास्ते की चौड़ाई ज्ञात कीजिए।
(a)8 m
(b) 7m
(c) 4m
(d) 2 m​

Answer 1

The breadth or width of the path is 2 m.

Step-by-step explanation:

The dimensions of the rectangular field :

Length, l = 20 m

Breadth, b = 15 m

∴ The area of the rectangular field = l * b = 20 * 15 = 300 m²

Let the equal breadth or the width of the path running all outside the field be “x” m.

Therefore, we have

The length of the field formed with the path = (20 + x + x) m = (20 + 2x) m

The breadth of the field formed with the path = (15 + x + x) m = (15 + 2x) m

∴ The area of the rectangular field formed with the path is,  

= (20 + 2x) (15 + 2x )  

= 300 + 40x + 30x + 4x²

= 4x² + 70x + 300

But, the area of the path is given = 156 m²

Also, we have

[Area of the rectangular field with path] – [Area of the rectangular field] = Area of path

Substituting the values  

⇒ [4x² + 70x + 300] – [300] = 156

⇒ 4x² + 70x - 156 = 0

⇒ 2x² + 35x – 78 = 0

⇒ 2x² + 39x – 4x – 78 = 0

⇒ x(2x+39) – 2(2x - 39) = 0

⇒ (2x +39)(x - 2) = 0

⇒ x = -39/2 or 2

Neglecting the negative value

⇒ x = 2 m ← breadth or the width of the path

------------------------------------------------------------------------------------------

Also View:

A rectangular garden 10m by 16m is to be surrounded by a concrete walk of uniform width.Given that the area of the walk is 120 square metres,assuming the width of the walk to be x,form an equation in x and solve it to find value of x ?

https://brainly.in/question/1092128

A rectangular field is 20m long and 14m wide. there is a path of equal width all around it.Having an area of 111 Sq. m. Find the width of the path.

https://brainly.in/question/6749776