A rectanular plot has been fenced with 500ft of wire. find the length and width of th plot if the length is 4 more than twice the width. Be sure to show both length and width along with units in your answer.
2007-07-04 02:51:41 · 9 answers · asked by newnew 1 in Science & Mathematics ➔ Mathematics
l = 4 + 2w
2l + 2w = 500
8 + 4w + 2w = 500
6w = 492
w = 82 ft
l = 168 ft
2007-07-04 02:58:53 · answer #1 · answered by Vipin A 3 · 0⤊ 0⤋
Since the rectangular plot has been fenced with 500ft of wire, we know the perimeter of the plot is 500ft. So we are trying to determine the measures of the length and the width. In order to do this we will use variables to represent the lengths of the sides, solve for the variable, and then plug in that value into the given sides.
OK, so let's represent the width as x, then the length is 2x+4 ( 4 more the twice the length of the width). we will plug these values into the equation of the perimeter of the rectangle.
2L+2W=P
2(2x+4)+2(x)=500
4x+8+2x=500
6x+8=500 (combine like terms)
6x=492
x= 82
so the length is 2x+4---->2(82)+4=168
width=x=82
"The length of the width is 82 and the measure of the length is 168"
2007-07-04 03:02:37 · answer #2 · answered by Carpe Diem (Seize The Day) 6 · 0⤊ 0⤋
Let the width of the plot be w ft.Hence the length of the plot is 2w+4 ft.
By the problem,
2(w+2w+4)=500 ft
or,3w+4=500/2=250
or,3w=250-4=246
or w=246/3=82
Therefore ,the width of the plot is 82 ft and the length is 82*2+4 or 168 ft.
2007-07-04 02:59:31 · answer #3 · answered by alpha 7 · 0⤊ 0⤋
perimeter (p) the sum of the sides of a rectangle
width (x)
length (y) ------> y = 4 + 2x -------> equation 1
p = 2x + 2y
p = 500 ft
therefore: 2x + 2y = 500ft
2(x+y) = 500ft
x + y = 250ft ---------> equation 2
substitute eqtn 1 in eqtn 2:
x + y = 250
x + (4 + 2x) = 250
3x + 4 = 250
3x = 246
x = 82 ft --------------> width
substitute the value of x in equation 1:
y = 4 + 2x
y = 4 + 2(82)
y = 168ft --------------> length
2007-07-04 03:05:17 · answer #4 · answered by armanomi 2 · 0⤊ 0⤋
If L= 2W+4 and 2L+2W= 500 ft., then:
2(2W+4) + 2W= 500
4W+8 +2W= 500
6W+8= 500
6W= 492
W= 82 ft. and then
L = 2(82) +4 so
L= 168 ft.
Check: 2( 82) + 2( 168) = 164 + 336 = 500
2007-07-04 03:24:12 · answer #5 · answered by Bomba 7 · 0⤊ 0⤋
well you have width (w) and length (2w+4) because you will double the width and add 4. perimeter is 2l+2w. sub in your length with 2w+4.
2(2w+4)+2w. multiply out.
4w+8+2w = 6w+8 = 500ft
6w = 492ft divide by 6
width = 82
now sub that into 2w+4
length = 168ft
2007-07-04 03:02:46 · answer #6 · answered by Adam 2 · 0⤊ 0⤋
Length = 168ft, Width = 82ft
2007-07-04 03:19:22 · answer #7 · answered by Gio 1 · 0⤊ 0⤋
Okay.
4W=L
4W+w(really l)=500
5w=500
divide on each side...
w=100
so back to the original equation..
4W=L
4(100)=L
400=L
You need to divide by 2 for each side
400/2= 200
So one side equals 200
100/2= 50
So the other side equals 50
So final answer:
Length=200 Width=50
2007-07-04 03:03:36 · answer #8 · answered by ravenesque0 3 · 0⤊ 0⤋
47 squared
2007-07-04 02:58:30 · answer #9 · answered by Anonymous · 0⤊ 2⤋