Question

7. 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 m², find
the width of the footpath.

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Answer 1

Answer:

let the width of the footpath is x m

now,area of the rectangular field is 32×24sq m

length of the field without path (32-x) m

width of the field without field (24-x) m

area of the field without path (32-x)(24-x) sq m

so, area of the path

32×24-(32-x)(24-x)=208

=> 32×24-(32×24-24x-32x+x^2)=208

=> 32×24-32×24+56x-x^2-208=0

=> x^2-56x+208=0

=> x^2-52x-4x+208=0

=> x(x-52)-4(x-52)=0

=> (x-52)(x-4)=0

x-52=0

x=52

again x-4=0

x=4

as the length of the field is 32 m then x is not equal to 52 m

so width of the footpath is 4 m

Answer 2

Step-by-step explanation:

${\large{\sf{\fbox{\orange{Question :→}}}}}$

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 m², find the width of the footpath.

$\\ \\ {\large{\sf{\fbox{\pink{Solution :→}}}}}$

• Length of field = 32 m
• Breadth of field = 24 m
• Area of path = 208 m²

Let's take the width be x,

$\\ {\bold{\bf{\fbox{\red{Area of path = Area of outer Rectangle - Area of inner Rectangle}}}}}$

Therefore,

208 = (32 × 24) - (32 - 2x)(24 - 2x)

208 = 768 - 768 + 64x + 48x - 4x²

4x² - 112x + 208 = 0

x² - 28x + 52 = 0

x² - 26x - 2x + 52 = 0

x(x - 26) - 2(x - 26) = 0

(x - 26) (x - 2) = 0

${\bold{\bf{\fbox{\purple{x \: = \: 26, 2}}}}}$

If w = 26, then breadth of inner Rectangle should be (24 - 52) = - 28 m which is not possible

Hence,

The width of the foothpath is 2m