The length of a rectangle is 1 in. more than twice its width. If the perimeter of the rectangle is 38 in., find the width of the rectangle. Define your variables, and show the equations you use. Solve the system of equations using the substitution method.
2006-10-05 07:59:53 · 12 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let L be the length, W the width. L=2W+1.
The perimeter P=2(L+W). Substitute L=2W+1, and you get P=2(2W+1+W)=2(3W+1)=6W+2.
Since P=38, you have 6W+2=38, so 10W=36, leaving W=6.
2006-10-05 08:03:01 · answer #1 · answered by James L 5 · 0⤊ 0⤋
Well, if the width is X, then the length is 2X+1, right?
And the perimeter is 2*length + 2*width.
substitute the 'X' expressions for width and length into the expression for perimiter and set it equal to 38.
Now you have an equation with one unknown, X, which you should be able to solve.
Try it, and come back if you still have trouble.
2006-10-05 15:03:52 · answer #2 · answered by Berry K 4 · 1⤊ 0⤋
2L + 2W = P ---> equation for perimeter of a rectangle
L = 2W + 1 ----> the length is 1 in more than twice the width
The the second equation and plug in the value of L into the perimeter equation
2L + 2W = P
2(2W + 1) + 2W = 38
now solve for W
4W + 2 + 2W = 38
combine like terms:
6W + 2 = 38
subtract 2 from both sides:
6W = 36
divide both sides by 6:
W = 6
the width is 6, so plug it into the second equation to find the L
L = 2W + 1
L = 2(6) + 1
L = 12 + 1
L = 13
the width is 6 and the length is 13
2006-10-05 15:23:00 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Let's say the width is A. The length is 1" more than twice its width, or 2A + 1.
Perimeter of a rectangle is 2A + 2 x (2A+1) = 38.
2A + 4A + 2 = 38
6A + 2 = 38
6A = 36
A = 6
Width = 6
Length = 13
2006-10-05 15:05:14 · answer #4 · answered by errant_hero 4 · 1⤊ 0⤋
let w = width of rectangle.
l = length
l = w+1
perimeter = 2w + 2l
so, replacing l with w+1,
38 = 2w + 2(w+1)
now simplify
38 = 2w + 2w +2
36 = 4w
w = 9
so the width is 9 in. and the length is 10 in.
now it's important to check your answer.
9 + 9 + 10 + 10 = 38 it's correct (yipeee!!)
keep practicing, you are going to get it ;_)
2006-10-05 15:03:48 · answer #5 · answered by ♪ ♫ ☮ NYbron ☮ ♪ ♫ 6 · 2⤊ 1⤋
x = length
y = width
x - 1 = 2y <-------- length is 1 in more than twice the width
x + x + y + y = 38 <----------------- perimeter is 38 in.
therefore, equation two becomes, 2x + 2y = 38
substitute equation 1 in equation 2............ 2x + x - 1 = 38
therefore, 3x = 39
x = 39/3
x = 13 in
substitute in equation 2 to get y
13 - 1 = 2y
12/2 = y
y = 6 in
good luck
2006-10-05 15:06:29 · answer #6 · answered by Liquid 3 · 1⤊ 0⤋
length=1 in
perimeter= 38 in
width= ?
sol:
perimeter= length*width
38=1*width
width=38/1-38 in ans
2006-10-05 15:03:34 · answer #7 · answered by siddharth 3 · 0⤊ 1⤋
1+2x+1+2x+2x=38
6x+2=38
6x=36
x=6
So the width is 6, the length is 1+2x which is 1+12 which equals 13
width=6
length=13
2006-10-05 15:05:24 · answer #8 · answered by Anonymous · 1⤊ 0⤋
let x be lengh
let y be width
x= 2y +1
2x + 2y = 38
substitute first eq to 2nd eq
2(2y +1) 2y = 38
4y + 2 + 2y = 38
6y = 38 - 2
6y = 36
y = 6 width
x = 2(6) =+1
x= 13
2006-10-05 15:09:31 · answer #9 · answered by oryyyo 2 · 1⤊ 0⤋
l=length, w=width & p=perimeter
l=2w+1
p=2l+2w=2(2w+1)+2w
38=4w+2+2w=6w+2
6w=38-2=36
w=6
width=6
length=2w+1=2*6+1=13
p=2l+2w=2*13+2*6=26+12=38
2006-10-05 15:04:23 · answer #10 · answered by yupchagee 7 · 1⤊ 0⤋