Question

A garden measuring 12m by 16m is to have a pedestrian pathway that is w meters
wide installed all the way around so that it increases the total area to 285 m². What
is the width of the pathway?​

Answer 1

Answer:

The answer is 1.5m

Step-by-step explanation:

Let EFGH be the park in which EF = 16m and FG = 12m.

Let the width of the path = xm

Now the length of rectangle ABCD = AB = (16 + 2x)m

Breadth of rectangle ABCD = BC = (12 + 2x)m

Now area of ABCD = 285m^2

AB x BC = 285

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

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

4x^2 + 56x - 93 = 0

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

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

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

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

x = 3/2  

x = 1.5 m

Answer 2

Step-by-step explanation:

19.5

15.5 hope it will help