A rectangle has a perimeter of 38 feet. The length is 1 foot less than 3 times the width. Find the dimensions of the rectangle.
Step-by-step explainations would be very helpful to me...thank you!
2007-03-29 07:23:56 · 7 answers · asked by aviator 5 in Science & Mathematics ➔ Mathematics
Perimeter Formula
P = 2L + 2W
38 = 2(3w - 1) + 2w
38 = 6w - 2 + 2w
38 = 8w + 2
38 + 2 = 8w - 2 + 2
40 = 8w
40 / 8 = 8w / 8
40 / 8 = w
5 = w
- - - -- - - -
The width is 5 feet
The length is 14 feet
- - - - - - - - - - -s-
2007-03-29 07:47:54 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
Perimeter is the distance around the rectangle
(width + width) + [(length) + (length)] = perimeter
(x + x) + [(3x - 1) + (3x - 1)] = 38
8x - 2 = 38 (Add up the like terms)
8x = 40 (Add 2 to both sides)
x = 5 (divide both sides by 8)
so 5 is the width so now the part length is 1 foot less than 3 times the width is:
3x -1 = length and x = 5 or width = 5
3(5) - 1 = length
length = 14
width = 5
length = 14
2007-03-29 07:33:47 · answer #2 · answered by Justin M 4 · 0⤊ 0⤋
5 x 14 ft
Call the length L and the width W.
If the perimeter is 38, then
2L + 2W = 38
(Perimeter is the length of a walk around the edge: L + W + L + W = 2L + 2W)
Now the length is one less than 3 time the width:
L = 3W - 1
Mulitply both sides by 2, and you have:
2L = 6W - 2
Substitute this into the first equation:
2L + 2W = 38
(6W - 2) + 2W = 38
6W + 2W - 2 = 38
8W - 2 = 38
8W = 40
W = 5
Now plug this value back into either of the equations:
L = 3W - 1
L = 3(5) - 1
L = 15 - 1
L = 14
Your dimensions are then 5 x 14 ft. Check:
5 is 1 less than 3 times 14.
The perimeter is 2L + 2W = 2(14) + 2(5) = 28 + 10 = 38.
2007-03-29 07:28:23 · answer #3 · answered by Phred 3 · 0⤊ 0⤋
P = perimeter
L = length
W = width
P = 2L + 2W (two lengths and two widths)
You're given that P = 38.
You're given that L = 3W - 1.
So work through the equations:
38 = 2L + 2W
38 = 2(3W - 1) + 2W
38 = 6W - 2 + 2W
38 = 8W - 2
40 = 8W
40/8 = 5 = W
P = 38 = 2L + 2W = 2L + 10
38 = 2L + 10
28 = 2L
28/2 = 14 = L
Check: 3 times the wid\th is 15, which is one more than the length of 14.
2007-03-29 07:32:23 · answer #4 · answered by Isaac Laquedem 4 · 0⤊ 0⤋
perimeter=2a+2b=38 a=3b-1 then 2(3b-1)+2b=38 then 6b-2+2b=38 8b= 40 b=5
a= 3(5) -1=14
2007-03-29 07:32:54 · answer #5 · answered by MadScientist 2 · 0⤊ 0⤋
the length=L,the width=W
3W-L =1---->L=3w-1
2(L+W)=38
substitute by L
2(4W-1)=38
4w-1=19
4w=20
W=5,L=14
2007-03-29 07:35:40 · answer #6 · answered by aziz wahba 1 · 0⤊ 0⤋
L+W+L+W = 38
L = 3W-1
from here make a substitution
2007-03-29 07:34:36 · answer #7 · answered by Jim M 3 · 0⤊ 0⤋