quadratic ques

Question

Roger mows half of a rectangular lawn that measures 40 m by 30 m by mowing strips of equal width around the perimeter. Cookie mows the small inner rectangle. how wide a strip should roger have so that they share work equally  

Answer 1

We are given that there is a rectangle (40m x 30m) in which there is another rectangle.

 

The Area of the given rectangle is 1200m², and the desired Area of the inner rectangle must be 600m² in order "that they share work equally."

 

let x = width of the strip, then, since Area = Length x Width,

we get 600m2 = (40m - x) • (30 - x)

expanding, we get 600 = 1200 - 70x + x²

combining terms, we get x² - 70x + 600 = 0

 

factoring, we get (x - 10)(x - 60) = 0

so, x can equal 10, or 60. But we will discard the 60 value because it is larger than the given dimensions.

 

so, x = 10m, and 40m - 10m = 30m; 30m - 10m = 20m

 

Thus, 30m • 20m = 600m²

 

the strip has to be 10m wide.