SOLUTION: The length of a rectangular garden is 5 feet longer than the width. The garden is surrounded by a 2 foot wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensi

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The length of a rectangular garden is 5 feet longer than the width. The garden is surrounded by a 2 foot wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensi      Log On


   

Question 111690: The length of a rectangular garden is 5 feet longer than the width. The garden is surrounded by a 2 foot wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden.
Found 2 solutions by malakumar_kos@yahoo.com, edjones:
Answer by malakumar_kos@yahoo.com(315) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangular garden is 5 feet longer than the width. The garden is surrounded by a 2 foot wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden.
let the width of the garden be = x ft
then length of the garden will be = (x+5) ft
Area of the garden = x(x+5) sqft
After including the measure of side walk on width &length we get the new
width & length of the entire garden as, width = (x+4) ft and
length = ((5+x+4) = (9+x) ft
Area of the side walk = Area of the entire garden - Area of the garden excluding the side walk
i,e 76 = (x+4)(x+9) - x(x+5)
76 = x^2+13x+36-x^2-5x
76-36 = 13x-5x
40 = 8x => x = 40/8 = 5 ft
dimensions of the garden is width = 5 ft and length = (5+5) = 10 ft

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
L=w+5 (garden)
L*w=A
w*(w+5)=w^2+5w (area of garden)
(w+4)*(w+5+4)=76+w^2+5w (area of garden plus sidewalk)
(w+4)*(w+9)=76+w^2+5w
w^2+13w+36=w^2+5w+76
8w=40 subtract w^2+5w+36 from each side.
w=5
L=5+5=10
Check
(5+4)*(10+4)=126
126-50=76
Ed