Algebra geometry

Question

the perimeter of a rectangular garden is 34 ft. the length is 3 ft more than the width. find the length and the width of the garden

Answer 1

The perimeter of a rectangle can be found by doing 2*width+2*length since a rectangle has two widths and two lengths.

We do not know the width or the length.

Let's call the width x

Then the length is 3 more than the width. So whatever the width is we find the length by adding 3. For example if the width is 2, then the length 2+3=5

So we can represent the length as the width +3 or x+3

Then plugging into our formula 2*width + 2*length

2*x + 2*(x+3) <- don't forget parenthesis!

we can distrubte the 2 to the x and the 3

2*x + 2*x + 2*3

or 2x + 2x + 6

or 4x + 6

Then we know the perimeter is 34 so

4x + 6 = 34

-6 -6 subtract 6 from both sides to balance

4x = 28

/4 /4 divide both sides by 4 to balance

x = 7

So the width = 7 and the length = 7+3 = 10

Lets check our answer if the side lengths are 7 and 10

Then the perimeter is 7+7 + 10 + 10 = 34

Answer 2

For a rectangle, the perimeter is the distance you would walk if you started at one corner and walker all the way around it. You would first walk the length, then the width, then the other length then the other width so:

P = l + w + l + w

P = 2l + 2w and since we are told that the perimeter is 34 ft then

2l + 2w = 34

We are also told that the length is 3 ft more than the width so l = w + 3. Since "l" and "w + 3" are the same, we can substitute "w + 3" in place of "l" in the first equation:

2(w + 3) + 2w = 34

2w + 6 + 2w = 34

4w + 6 = 34

4w = 28

w = 7

Since l = w + 3, then l = 7 + 3 = 10

So the length is 10 ft and the width is 7 ft