A rectangular garden having a dimensions of 26 ft. by 30 ft. is surrounded by a walk of uniform width. If the area of the walk is 240 ft2 , what is its width?

Answer 1

26 x30 = 780 square feet for the garden area

240 square feet for the surrounding walk area

total area = 780 + 240 = 1020 ft^2

1020 = (26+2w)(30+2w) = 780+ 60w+52w + 4w^2

4w^2 + 112w + 780 = 1020

divide by 4

w^2 + 28w + 156 = 245

w^2 + 28w = 60

w^2 + 28w +14^2 = 60 + 14^2

(w+14)^2 = 60+196= 256

w+14 = + or - sqr256 = 16

w = 16 - 14 = 2 feet wide walkway

w= 2 ft

check the answer and see if that gives 240 ft^2 for the walkway area:

(26+2w)(30+2w)

= (26+4)(30+4)

= 30(34) = 1020

1020-26(30)

=1020-780

= 240 ft^2 = walkway area

walkway area = walkway area on 2 sides + walkway area on the other two sides + 4 times the width squared for the 4 corner walkway areas

26(2)(2) + 30(2)(2) + 4(2)(2)

= 104 + 120 + 16 = 240 ft^2

or twice the sum of one strip of the walkway including the corner areas + another strip without the corner areas

2[(26+2w)w + (30)w]

=2(2w^2 + 56w)

=2(2(2)^2 + 56(2))

=2(8+112)

=2(120)

=240 ft^2