Question

A footpath of uniform width runs all around the inside of a rectangular field 28 m long and 22 m wide. If the path occupies 600 $m^2$, what is the width of the path?

• A. 26cm²
• B. 24cm²
• C. 36cm²
• D. 40cm²

Answer 1

The correct option is A

26cm²

EH=GF = $(22-2x)$ m

EF =GH =$(28-2x)$ m

Let the width of the path be ${}^{\prime }{x}^{\prime }$ m.

Area of the path =Area (ABCD)-Area (EFGH)

$600=(28\times 22)-(28-2x)(22-2x)$

$600=28\times 22-28\times 22+56x+44x-4x^2$

$\Rightarrow 4x^2-100x+600=0$

$\Rightarrow x^2-25x+150=0$

$\Rightarrow x^2-15x-10x+150=0$

$\Rightarrow x(x-15)-10(x-15)=0$

$\Rightarrow (x-10)(x-15)=0$

$\Rightarrow x=10$ or $x=15$

$x$ can't be 15 be cause $(22-2x)$ and $(28-2x)$ both will be negative.

$\therefore x=10$ or width of the path =10 m.