I need help with a word problem

Question

You wish to build a concrete walk around your garden that measures 12 meters by 16 meters to enlarge the total area to 285 square meters. What will be the width of the walk?

Answer 1

x=width of the walk

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

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

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

4x^2+56x-93=0

factor

4*93=2*2*3*31=(2*3)*(2*31)=6*62 and 62-6=56

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

2x-3=0

2x=3

x=3/2

x=1.5 feet is the width of the walk

Answer 2

now , the area of the garden is 12x16 = 192 square meters , the required new area after the enlarging is 285 square  means that the new area of the walk is 285-192=93  and since 285 is 15x19 ,since the garden is rectangle ,we must add the width of the walk to all sides of the rectangle , so we have to add same measure 2 times to 12 ,and 2 times to 16 ,and that measure has to be 1.5 meters since 1.5 +12+1.5 =15 ,and 1.5+16+1.5 =19 ,so the width of the new walk has to be 1.5 meters.