Finding the width of a rectangle the hard way?

Question

The length of a rectangle is 1 in. more than twice its width. If the perimeter of the rectangle is 50 in., find the width of the rectangle. Solve using an algebraic equation

Answer 1

I'm a bit rusty, but see if you can follow this.

L=Length W=Width

L=2W+1

2W+2(2W+1)=50 (Perimeter)

2W+4W+2

6W+2=50

6W=48

W=8

L=17

Answer 2

well, you know it's one more than twice the width so it's 2 and use "w" for width and set this up. 2w + 1 on the top and bottom. then 2w on each of the sides. and add up all your "w's" and your single digit numbers and you should get, 8w + 2 and set that equal to 50. 8w + 2=50
-2 -2
8w=48
divide by 8
w = 6, you're not done yet though. Plug your 6 back into your problem. Your length should be 12 on each side-2 (times your width, which is 6) =12. and you should have the same for the other side. Then for the top and bottom you should have 2(6) +1 =13. you should have 13 for the top and bottom. You can go back and check your answer so that it fits with your perimeter. 12+12+13+13, and it does 50=50. and there you have it! Hope that helps. =)

Answer 3

OK
L = 2w+1 ;

Perimeter = 2L + 2w

50 = 2(2w+1) + 2w
50 = 4w + 2 + 2w
50 = 6w +2
48 = 6w
8 = w

SO the width is 8 and the length:
L = 2(8) + 1
L = 16+1 = 17.

Check
17 + 17 + 8 + 8 = 50?
34 + 16 = 50?
50 = 50 YES!!

Hope that helps.

Answer 4

Let the width of rectangle= w
Length of rectangle= 2w +1
Perimeter of rectangle= 2{ Length of rectangle +width of rectangle. 2{ 2w+1+w}.=50in.
6w=48. w=8in. L= 16+1=17
Ans. Length of rectangle= 17in.
width of rectangle = 8in.

Answer 5

Let L be the length, and W be the width.
L = 1 + 2W......(1)
Half of the perimeter is,
L+W = 50/2 = 25......(2)
(1) - (2): -W = 2W-24
W = 8 in
L = 1+2*8 = 17 in

Answer 6

u need to make an equation with "w", "2w + 1", and it equaling 50 so its gonna look like this:

2(2w + 1) + 2(w) = 50

then u need to distribute:

4w + 2 + 2w = 50

then u need to simplify:

6w + 2 = 50

now u need to get the 2 over with the 50 by subtraction:

6w = 48

then u need to get "w" by itself by dividing 48 by 6 and u get:

w = 8

and thats ur width! hope this helped!

Answer 7

perimeter = 2W+2L

so,

1a) 2W + 2(2W+1) = 50
1b) 2W + 4W + 2 = 50
1c) 6W = 48
1d) W = 8
1e) so, L = 2 x 8 + 1 = 17

checking, (2 x 8) + (2 x 17) = 50

Answer 8

l = 2w+1
2l + 2w = 50

Substituting the first equation intoi the second,

4w + 2 + 2w =50

6w = 48
w = 8
so
l=17

Answer 9

2x+1 (twice) = lenghts
x (twice) = width

thefore permiter = (2x +1) + (2x +1) + x + x = 6x+2 = 50 inches

therefore 6x = 48

Therfore x = 8

width is 8 inches

length is 17 inches

Answer 10

y work it out the hard way if you can work it out the easy way