Question

Can someone help me with my question for once?

'Write an equation to solve the following. Show all your work, including the steps for solving the equation and checking your answer.' -The perimeter of a rectangular photo is 72 cm. The length is twice the width. What are the length and width of the photo?-

I have no idea how to find sides.

Answer 1

Hold on.......

Answer 2

Okay q.q thanks..

Answer 3

i believe its 144, since 72 times 2 = 144 :)

Answer 4

144 is what? You get the perimeter by adding up all the sides. 2w, +2l. How could it be 144? O-O

Answer 5

I just don't understand how to derive the sides out of the perimeter

Answer 6

Let's write an equation and solve the equation.

Answer 7

A drawing can be helpful.

Answer 8

Yes please. xd

Answer 9

We are told the length is twice the width.
Let's choose a variable to represent the width.
Which variable would you like to use to represent the width?
(A variable is usually represented by a letter.)

Answer 10

You can use w (for width), x, or any other letter you like.

Answer 11

Let's go with x.?

Answer 12

Great. The width is x. It is unknown.
Let's add x to our figure.

Answer 13

We are told that the length is twice the width.
Using math symbols (variables), if the width is x, what is twice the width?

Answer 14

Twice the width would be x(2)?

Answer 15

Very good. We multiply the width, x, by 2.
We could write it as x * 2, or x(2), but the more common way to write it is as 2x.

Answer 16

Now we can also add that to our figure.

Answer 17

As you can see, we have in our figure a rectangle with unknown width, x, and unknown length, 2x.

Answer 18

Now we use the other fact given to us in the problem.
The perimeter of the rectangle is 72 cm.

Answer 19

Do you know what the perimeter means?

Answer 20

The perimeter means each side added to a total. Or length times two, and width times two.

Answer 21

Excellent. That is exactly it, and you even explain it in two different ways.

Answer 22

Slowly but surely.

Answer 23

Using our width of x and our length of 2x, let's write an expression for the perimeter.
We can use your first explanation of perimeter which is to simply add all side lengths.

Perimeter = x + x + 2x + 2x

You follow so far?

Answer 24

So, 72=x+x+2x+2x?

Answer 25

We are told the perimeter is 72 cm.
Since the perimeter is x + x + 2x + 2x, and the perimeter is also 72 cm, then

x + x + 2x + 2x = 72

That is the equation we need to find the width, x.

Add all like terms on the left side.
Then divide both sides by the coefficient of x to find x.
That will give you x, the width.

Since the length is twice the width, multiply x by 2 to find the length.

Answer 26

Exactly.

Answer 27

I'm sorry, my computer must be lagging because I'm getting your responses late. >.<

Answer 28

I know, mine is slow too.

Answer 29

Now add all the x terms.
Remember that x is the same as 1x.
For example, x + 3x = 1x + 3x = 4x
What is x + x + 2x + 2x = ?

Answer 30

It would be, 1x+1x+2x+2x=6x?

Answer 31

Correct.
That means you now have
6x = 72
You want x alone, but x is being multiplied by 6.
You need to divide 6x by 6 to have x alone.
You must do the same operation to both sides of an equation, so divide both sides by 6.