Question

. A garden measuring 12 m by 16 m is to have a pedestrian pathway that is ???????? meters wide installed all the way

around it, increasing the total area to 285 m2. What is the width, ????????, of the pathway?

Answer 1

1.5m

Explanation:

Let the length of the pathway across all its side be x. This means we are adding a length of 2x to both the length and breadth to 12+2x and 16+2x respectively.

The new area thus becomes:

(12+2x)(16+2x) = 285

24x + 32x + 192 + 4x^2 = 285

4x^2 + 56x + 192 = 285

4x^2 + 56x + 192 - 285 =0

4x^2 + 56x -93 = 0

4x^2 + 62x - 6x - 93 = 0

2x( 2x + 31) - 3(2x + 31) = 0

(2x - 3)(2x + 31) = 0

This means x = 3/2 or -31/2

Since length cannot be negative , we choose the first and neglect the second meaning our answer is 3/2 which is 1.5 meters