Question

A foot path of uniform width runs all around inside of a rectangular field 45 m long and
36 m wide. If the area of the path is 234 m², find the width of the path.
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Answer 1

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Answer 2

Consider ABCD as a rectangular field having

Length = 50 m

Breadth = 38 m

We know that

Area of rectangular field ABCD = l × b

Substituting the values

= 50 × 38

= 1900 m2

Let x m as the width of foot path all around the inside of a rectangular field

Length of rectangular field PQRS = (50 – x – x) = (50 – 2x) m

Breadth of rectangular field PQRS = (38 – x – x) = (38 – 2x) m

Here

Area of foot path = Area of rectangular field ABCD – Area of rectangular field PQRS

Substituting the values

492 = 1900 – (50 – 2x) (38 – 2x)

It can be written as

492 = 1900 – [50 (38 – 2x) – 2x (38 – 2x)]

By further calculation

492 = 1900 – (1900 – 100x – 76x + 4x2)

492 = 1900 – 1900 + 100x + 76x – 4x2

On further simplification

492 = 176x – 4x2

Taking out 4 as common

492 = 4 (44x – x2)

44x – x2 = 492/4 = 123

We get

x2 – 44x + 123 = 0

It can be written as

x2 – 41x – 3x + 123 = 0

Taking out the common terms

x (x – 41) – 3 (x – 41) = 0

(x – 3) (x – 41) = 0

Here

x – 3 = 0 or x – 41 = 0

So x = 3 m or x = 41 m which is not possible

Therefore, width is 3 m.

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