The length of a rectangle is 2 in. more than twice its width. If the perimeter of the rectangle is 46 in., find the width of the rectangle.
2007-09-15 03:06:36 · 10 answers · asked by PJH 2 in Science & Mathematics ➔ Mathematics
Perimeter Formula
P = 2L + 2W
Let
w = width
2w + 2 = Length
46 = perimeter
The equation
46 = 2(2w + 2) + 2w
The distributive property on the right side of the equation.
46 = 4w + 4 + 2w
Colllect like terms
46 = 6w + 4
Transpose 4
46 - 4 = 6w + 4 - 4
Collect like terms
42 = 6w
Divide both sides of the equationby 6
42 / 6 = 6w / 6
42/6 = w
7 = w
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The width is 7 inches.
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2007-09-15 03:21:06 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
Hi,
Let x = width
Then 2x + 2 = length
Since perimeter = 2Length + 2width, then
46 = 2(2x + 2) + 2x
46 = 4x + 4 + 2x
46 = 6x + 4
42 = 6x
7 = x This is the width.
That means the length of 2x + 2 = 2(7) + 2 or 16.
So 2L + 2W = 2(16) + 2(7) = 32 + 14 = 46, the perimeter
I hope that helps!! :-)
2007-09-15 10:14:39 · answer #2 · answered by Pi R Squared 7 · 0⤊ 0⤋
If you don't understand word problems, you need to rewrite the question so you can understand it
So put it into a form you can understand, ie an equation.
If the width is x in. then the length must be x+2.
You have 4 sides, 2 width and 2 length.
x+2
------------------------
|............................. |
x|............................. | x
| ............................ |
------------------------- (ignore the dots, they are there to put the rectangle in place)
x+2
So: x+x+2+x+x+2 = perimeter therefore = 46.
Now you have an equation: 46 = 4x + 4 (because there are 4 lots of x and 2 lots of 2)
And there you go, now you can work it out :)
2007-09-15 10:25:59 · answer #3 · answered by atomixandie 2 · 0⤊ 0⤋
the width is 7,the length is 16
2007-09-15 10:14:18 · answer #4 · answered by hummy 1 · 0⤊ 0⤋
length of the rectangle = y
width of rectangle = x
The perimeter is 46 in ==> 2x + 2y = 46
y = 23 - x
The length is 2in more than twice its width ==> y = 2x + 2
y = y, so 2x + 2 = 23 - x, and from there on you just solve to find the value of x.
-----------------------------------------
2x + 2 = 23 - x
3x = 21
x = 7
Answer: The width of the rectangle is 7 in.
2007-09-15 10:11:48 · answer #5 · answered by Chameleon 2 · 0⤊ 0⤋
2L+2W = 46
L = 2W+2 => 4W+4+2W = 46
6W = 42
W = 7
And L = 14 + 2 = 16
2007-09-15 10:15:44 · answer #6 · answered by Words Of Wisdom 3 · 0⤊ 0⤋
L = 2 in + 2*W
W = width
perimeter = 2*L + 2W = 46
46 = 2*(2+2W)+2W
46 = 4+4W+2W
42 = 6W
W = 42/6
2007-09-15 10:13:49 · answer #7 · answered by hello 1 · 0⤊ 0⤋
l=length, w=width, p=perimeter
l=2+2w
p=2l+2w=46
2(2+2w) +2w =46
4+4w+2w=46
6w=42
w=7
2007-09-15 10:17:58 · answer #8 · answered by bignose68 4 · 0⤊ 0⤋
looks like there are experts in these sort of problems..u r lucky enough!
2007-09-15 10:21:27 · answer #9 · answered by murthy 3 · 0⤊ 0⤋
2L+2L+4=46
4L=42
L=10.5
2007-09-15 10:16:37 · answer #10 · answered by JAMES 4 · 0⤊ 0⤋