Question

A garden area is 30 ft long and 20 ft wide. A path of uniform width is set inside the edge. If the remaining garden is 400ft^2, what is the width of the path?

Answer 1

2.19 ft ( approx )

Explanation:

Let x be the width ( in ft ) of the path,

Given,

The dimension of the garden area,

Length = 30 ft, width = 20 ft,

So, the dimension of the remaining garden ( garden excluded path ),

Length = (30 - 2x) ft, width = (20-2x) ft

Thus, the area of the remaining garden,

A=(30 - 2x)(20 - 2x)

According to the question,

A = 400 ft²,

`(30 - 2x)(20 - 2x)=400`

`600-60x -40x + 4x^2= 400`

`4x^2-100x+600-400=0`

`4x^2-100x+200=0`

`x^2-25x+50=0`

By the quadratic formula,

`x=(-(-25)\pm √((-25)^2-4* 1* 50))/(2)`

`=(25\pm √(625-200))/(2)`

`=(25\pm √(425))/(2)`

`\implies x = (25+ √(425))/(2)\text{ or }x=(25- √(425))/(2)`

⇒ x ≈ 22.8 or x ≈ 2.19,

∵ Width of the path can not exceed 30 ft or 20 ft

Hence, the width of the path is approximately 2.19 ft.