SOLUTION: The length of a rectangular park is 2 times greater than its width.
The park is framed by sidewalk that is 2 m wide.
The area of the park is increased by 136m square if the s
Question 173103: The length of a rectangular park is 2 times greater than its width.
The park is framed by sidewalk that is 2 m wide.
The area of the park is increased by 136m square if the sidewalk is included.
What is the area of the park without the surrounding sidewalk ?
Show the work.
You can put this solution on YOUR website! The length of a rectangular park is 2 times greater than its width.
The park is framed by sidewalk that is 2 m wide.
The area of the park is increased by 136m square if the sidewalk is included.
What is the area of the park without the surrounding sidewalk ?
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area of sidewalk is 136 sq m
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"area of park plus walk" is
.
Park measurements:
Let w = width of park
then
2w = length of park
.
Park plus walk measurements:
w+4 = width
2w+4 = length
.
(w+4)(2w+4) - w(2w) = 136
2w^2+4w+8w+16 - 2w^2 = 136
4w+8w+16 = 136
12w+16 = 136
12w = 120
w = 10 m (width)
.
Length:
2w = 2(10) = 20 m(length)
You can put this solution on YOUR website! L=2W
AREA OF PARK=LW
AREA OF PARK=2W*W=2W^2
AREA WITH SIDEWALK=(2W+2*2)(W+2*2)
AREA WITH SIDEWALK=(2W+4)(W+4)
AREA WITH SIDEWALK=2W^2+12W+16
(2W^2+12W+16)-(2W^2)=136
12W=136-16
12W=120
W=10 M.
L=2*10=20 M.
PROOF:
20*10=200 M^2 FOR THE PARK
(20+4)(10+4)=200+136 M^2 FOR THE PARK PLUS THE SIDEWALK.
24*14=336
336=336
You can put this solution on YOUR website! area of sidewalk is 136 sq m
Park measurements:
Let w = width of park
then
3w = length of park (2 times greater is 3 times as much)
If it were 1 time greater, that would be 2x. 2x greater is an increase of 2, for a total of 3)
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Park plus walk measurements:
w+4 = width
3w+4 = length
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(w+4)(3w+4) - w(3w) = 136
3w^2+4w+12w+16 - 3w^2 = 136
4w+12w+16 = 136
16w+16 = 136
16w = 120
w = 7.5 m (width)
Length = 3w = 22.5 m
Area = 7.5*225 = 168.75 sq meters
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