The width of a rectangle is 584 feet shorter than five times its length. The perimeter of the rectangle is 512.
The optional answers are:
140 feet
116 feet
18,230 square feet
2007-01-12 02:04:34 · 5 answers · asked by miss.priss534 1 in Science & Mathematics ➔ Mathematics
Let L = length of rectangle.
Since the width of the rectangle is 584 feet shorter than 5 times its length,
W = 5L - 584
The perimeter of a rectangle is given by the formula
P = 2L + 2W
But W = 5L - 584, so
P = 2L + 2[5L - 584]
P = 2L + 10L - 1168
P = 12L - 1168
But we know that P = 512, so
512 = 12L - 1168
512 + 1168 = 12L
1680 = 12L, therefore
L = 1680/12 = 840/6 = 420/3 = 140
2007-01-12 02:10:44 · answer #1 · answered by Puggy 7 · 0⤊ 0⤋
Let's define the length of the rectangle as X.
From the problem, you can define the width in terms of X.
From there, you add the width and the length accordingly to match the perimeter. Since they give you the perimeter, you can solve for the length X of the rectangle.
2007-01-12 02:14:13 · answer #2 · answered by wheresdean 4 · 0⤊ 0⤋
width = x
length = y
x = 5y - 584
The perimeter is 512, so 2x +2y = 512 or x + y = 256
y =256-x
substitute the new term for y into the first equation:
x = 5(256-x) - 584
x = 1280 -5x - 584
6x = 696
x= 116
y = 256-116
y = 140
Width = 116
Length = 140
2007-01-12 02:17:37 · answer #3 · answered by borscht 6 · 0⤊ 0⤋
w = width
l = length
given:
w = 5l - 584
2w + 2l = 512
then combining:
2(5l - 584) + 2l = 512
10l - 1168 + 2l = 512
12l = 1680
l = 140 ft
2007-01-12 02:12:35 · answer #4 · answered by Patrick 5 · 0⤊ 0⤋
5L = W + 584
and
2L + 2W = 512.
....solve for L and W.
The answer for W is 116 ft.
2007-01-12 02:11:33 · answer #5 · answered by julka323 3 · 0⤊ 0⤋