Algebra Homework Help?

Question

The length of a rectangular playing field is 5ft less than twice its width. If the perimeter of the playing field is 230 ft, what is the length and width of the field?

I'm having difficulty in finding how to set up and work this problem.

Answer 1

Because the Length (L) is 2 Width (W) Minus 5...
L = 2W - 5
and
2L + 2W = 230
Substitute L....
So
2(2W - 5) + 2W = 230
4W - 10 + 2W = 230
6W - 10 = 230
6W = 240
W = 40
So...
2L + 2(40) = 230
2L + 80 = 230
2L = 150
L = 75

So Finally...
L = 75, W = 40!

To check plug it in...

2L + 2W = 230
2(75) + 2(40) = 230
150 + 80 = 230
230 = 230

So yes...

L = 75, W = 40

Answer 2

Let's set it up like this:
L= length of the field
W= width of the field
2 x W - 5 = L is your equation: the length is 5 feet less than twice (two times) the width.

Now the perimeter (total distance around the field if you walked it) is 230 feet. Since we only need to know the total length and total width we know that the length plus width is one half of the perimeter: 115 feet

L = 2 x W - 5 and that L + W = 115 and therefore L = 115 - W
using algebra we canshow the new equation as:
115 - W = 2 x W - 5
120 = 3 x W
40 = W
So plug in our solution for W into the first equation:

L = 2 x 40 - 5
L= 80 - 5
L = 75 and W = 40

Check it so that 75 + 75 + 40 + 40 = 230 which is the perimeter

Answer 3

L for length
w for width

L = 2w - 5

Perimeter of a rectangle is 2L + 2W = 230ft

so..

2( 2w -5) + 2w = 230 ft
4w - 10 + 2w = 230ft
6w = 240 ft
w = 40

use the value of width to get the length. =)