Question

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

Answer 1

The width of path is 1.5 m

Explanation:

We are given the following in the question:

Field:

Length = 45 m

Width = 35 m

Area of filed =

`\text{Area} = \text{Length}* \text{Width} = 45* 36 = 1620`

The area of rectangular field the is 1620 square meter.

Area of path = 234 m

Let x be the width of path.

Area of field without path = 1620 - 234 = 1386 square meter.

Now, dimensions of field without path is:

Length =
`45 -x - x = 45 -2x`

Width =
`36 -x - x = 36 - 2x`

`\text{Area} = \text{Length}* \text{Width}`

Thus, we can write:

`(45-2x)(36-2x) = 1386`

`1620 - 90x - 72x + 4x^2 = 1386\\4x^2 - 162x + 234 = 0\\2x^2 - 81x + 117 = 0\\(2x - 3)(x - 39) = 0\\x = 1.5, x = 39`

We cannot take the width as 39 m, thus, the width of path is 1.5 m.