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

Answer:

2.19 ft ( approx )

Step-by-step 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,

$x=\frac{-(-25)\pm \sqrt{(-25)^2-4\times 1\times 50}}{2}$

$=\frac{25\pm \sqrt{625-200}}{2}$

$=\frac{25\pm \sqrt{425}}{2}$

$\implies x = \frac{25+ \sqrt{425}}{2}\text{ or }x=\frac{25- \sqrt{425}}{2}$

⇒ 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.