The length of a rectangular field is 50 meters more than twice its width. If the perimeter is 700 meters, find the dimensions of the field.
How would you work this problem out?
2007-06-06 18:37:46 · 8 answers · asked by snowflak_04 1 in Science & Mathematics ➔ Mathematics
L = 2w+50
2L + 2w = 700
using substitution:
2(2w+50) + 2w = 700
4w + 100 + 2w = 700
6w + 100 = 700
6w = 600, w = 100
L = 2w+50 so L = 2(100) + 50 = 250
Check: 2(250)+2(100) = 700
True, so answer is correct.
2007-06-06 18:46:34 · answer #1 · answered by Kate v.7.0 6 · 3⤊ 0⤋
Let w = width of the rectangular field
l = length of the rectangular field
Since length is 50 meters more than twice its width,
l = 50 + 2w
Perimeter is 700 m
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Formula for perimeter of a rectangle is
P = 2l + 2w
700 = 2(50 + 2w) + 2w
700 = 100 + 4w + 2w
700 = 100 + 6w
700 - 100 = 100 - 100 + 6w
600 = 6w
600/6 = 6w/6
100 = w
w = 100 m ==> width of the rectangular field
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Substitute the value of w to find l
700 = 2l + 2w
700 = 2l + 2(100)
700 = 2l + 200
700 - 200 = 2l + 200 -200
500 = 2l
500/2 = 2l/2
250 = l
l = 250 m ==> length of the rectangular field
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Good luck!
2007-06-07 01:51:26 · answer #2 · answered by detektibgapo 5 · 0⤊ 0⤋
L = 50 + 2W
Perimeter: 2L + 2W = 700
Substitute L into the Perimeter formula,
2(50 + 2W) + 2W = 700
100 + 4W + 2W = 700
6W = 700 - 100 = 600
Width, W = 600/6 = 100m
Length, L = 50 + 2(100) = 250m
2007-06-07 01:47:04 · answer #3 · answered by jurassicko 4 · 0⤊ 0⤋
Let width be x m and length be (2x + 50) m
Perimeter = 700 m
2(x + 2x + 50) = 700
2(3x + 50) = 700
6x + 100 = 700
6x = 600
x = 100
2x + 50 = 250
The field is 100m wide by 250 m long
2007-06-07 02:16:35 · answer #4 · answered by Akilesh - Internet Undertaker 7 · 0⤊ 0⤋
By forming two equations from the given information.
L=2w+50
2L+2w=700
Substituting
2(2w+50)+2w=700
4w+100+2W=700
6W=600
W=100
L=2(100)+50=250
2007-06-07 01:48:47 · answer #5 · answered by jess959 1 · 0⤊ 0⤋
Hi. Start with the limiting dimension, 700. Divide by two (350) to find the total length of the two sides of a right triangle. Just a hint.
2007-06-07 01:43:25 · answer #6 · answered by Cirric 7 · 0⤊ 1⤋
2w+50=L ...................2(w+L)=700
2w+50=L.....................w+L=350
2w+50=L.....................w=350-L
...........2(350-L)+50=L
...........700-3L+50=0
...........3L=750
...........L=25....................w=350-25 = 325
.............L=25, w=325
lol i think i messed up
2007-06-07 01:47:36 · answer #7 · answered by driftaddict87 4 · 0⤊ 1⤋
2,500?
2007-06-07 01:47:20 · answer #8 · answered by aissa benitez 1 · 0⤊ 1⤋