SOLUTION: A flower bed is in the shape of a rectangle. Its length is twice its width. The bed is surrounded by a walkway 4 feet wide. If the area of the walkway is exactly twice the area

Question 4462: A flower bed is in the shape of a rectangle. Its length is twice its width. The bed is surrounded by a walkway 4 feet wide. If the area of the walkway is exactly twice the area of the bed, find the dimensions of the bed.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Begin by drawing a rectangle whose width is x, and whose length is 2x. Add another rectangle outside this rectangle that extends 4 feet in each direction from the inner rectangle. The width of the outer rectangle is x+8, and the length of the outer rectangle is 2x+8, since you have to add 4 feet TWICE in each direction.

The area of the inner rectangle is LW = x(2x) or .
The area of the outer rectangle is LW = (x+8)(2x+8) or .
Area of walkway = outer area - inner area
=
=

Equation: Area of walkway equals twice inner area (area of the bed):
.

Quadratic equations, so set equal to zero by subtracting 24x and 64 from both sides.

Factor out the common factor of 4:

Factor the trinomial:

Solutions are x = 8 and x = -2, but x represents the side of a rectangle, so it cannot be negative.

Final answer:
x = 8 width of bed.
2x = 16 length of bed.

Check:
Dimensions of the walkway
x+8 = 16
2x+8= 24
Area of bed = = 128 sq. ft.
Total area = = 384 sq. ft.
Area of walk = 384 - 128 = 256 sq. ft.

Area of walk = 2(area of bed)
256 = 2(128)

R^2 at SCC
RELATED QUESTIONS
Please help me solve this word problem: The length of a rectangular flower bed is 3... (answered by 067isa,checkley71,TakeATuition.com)

susan built a flowerbed. the perimeter of the flower bed is 42 feet, and its length is 9... (answered by ewatrrr)

The length of a rectangle flower bed is 7 feet less than 3 times its width. The area of... (answered by solver91311)

A rectangular flower bed with width 12 feet and length 15 feet is going to have a walkway (answered by CharlesG2)

A rectangular lawn measuring 8 m by 4 m is surrounded by a flower bed of uniform width.... (answered by ikleyn)

A 60 by 80-foot rectangular walk in a park is surrounds a flower bed. If the walk is of... (answered by ankor@dixie-net.com)

The length of a rectangular flower bed is 11 feet less than 3 times its width. The area... (answered by graphmatics)

A rectangular flower bed is eight feet longer than it is wide. If the area of the flower... (answered by checkley77)