A rectangular yard is surrounded by a fence that is 4 feet longer than it is wide. If the perimeter of the fence is 424 feet, what are the dimensions of the yard it encloses.
2006-12-01 15:33:59 · 7 answers · asked by SweetnSpiceyBrown 2 in Science & Mathematics ➔ Mathematics
Since the fence surrounds the yard, the length of the fence is 424 feet.
Let x be the width of the fence.
So the length of one width = x
Length of second width = x
Length of front side = x + 4
Length of back side = x + 4
Total Parameter length = sum of all sides
Total Parameter length = x + x + (x+4) + (x+4)
Total Parameter length = 4x + 8
Total Parameter length = 4x + 8 = 424 feet (given).
4x + 8 = 424 feet
4x = 424 - 8 feet
4x = 416 feet
x = 416/4 feet
x = 104 feet
x + 4 = 104 + 4 = 108 feet.
Width is 104 feet.
Length is 108 feet.
2006-12-01 15:53:28 · answer #1 · answered by Brenmore 5 · 0⤊ 0⤋
first, only use one variable x
let the width = x and length = x + 4
the perimeter = 2(x) + 2(x + 4) = 424 feet
so...4x + 8 = 424 feet
x = 104 feet
--length =(x + 4)= *108 feet*
--width = x = *104 feet*
*the dimensions of the yard it encloses is 104 feet by 108 feet*
2006-12-01 23:49:52 · answer #2 · answered by jonnyjack 2 · 0⤊ 0⤋
The perimeter is equal to the lenght +Lenght + width+width..
Perimeter = 424 feet= (x+4) + (x+4) + X + x
bring the 4's over and substract them from 424
424-4-4=4x
416= 4x
Divide 416 by x to get x = 104...
so your length will be 104 and your width will be 108 (104 +4)
2006-12-01 23:38:36 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Let's first start with the equation for perimeter of a rectangle.
P=2l +2w where l is length and w is width.
Now, state the given information.
l = w + 4
P = 424
Using our definition of l and our definition of P, use substitution with the equation of the perimeter of a rectangle:
P = 2l +2w
424 = 2(w+4) + 2w
Then, solve for w:
212 = w+ 4 + w
208 = 2w
104 = w
Now plug this back in to the definition of l:
l=w+4
l=104+4
l=108
2006-12-01 23:41:14 · answer #4 · answered by Lucan 3 · 0⤊ 0⤋
let x be the width of the yard
therefore the length would be x+4
now perimeter is 424
hence the equation would be
x+x+x+4+x+4=424
4x+8=424
4x=424-8
4x=416
x=104
verify by substituting value of x
2006-12-01 23:47:39 · answer #5 · answered by amank 2 · 0⤊ 0⤋
Two equations:
L = W + 4
2L + 2W = 424
2006-12-01 23:38:50 · answer #6 · answered by arbiter007 6 · 0⤊ 0⤋
P = 2L + 2W
L = W + 4
P = 2(W + 4) + 2W
P = 2W + 8 + 2W
P = 4W + 8
424 = 4W + 8
4W = 416
W = 104
L = W + 4
L = 104 + 4
L = 108
2006-12-01 23:39:54 · answer #7 · answered by Anonymous · 0⤊ 0⤋