Finding width

Question

A public garden measures 12yd by 16yd is to have a pedestrian walkway installed around the perimeter.  The new area of the garden will be 285 yd² The width of the walkway will be how many yards wide?

Answer 1

The Area of the larger rectangle is 285y²

We know that Area = Length x Width

 

let x = the width of the walkway

 

then Area = (16 + x)(12 + x) = 285y²

 

then, 285y² = x2 + 28x + 192

 

rearranging, x2 + 28x - 93y² = 0

this equation cannot be factored, so we must use the quadratic formula

our formula becomes (-28 ± √282 - 4•1•-93)/2•1

which becomes (- 28 ± 34)/2

we can see that the minus value must be discarded because length cannot be negative

so, our solution becomes (-28 + 34)/2 = 3y

 

Proof: (16+3)(12+3) = 19•15 = 285y²