The length is 35 yards and the perimeter is 120, what is the area?
You have should know two equations by this point in math: Area and Parameter.
In this problem you're going to combine them. To do this let's first list our two equations.
Area = length * width
Parameter = (2 * length) + (2 * width)
Do you see anything these two equations have in common? They both share the same two variables: length and width.
The next thing you do is list what you have. Here it is:
Parameter = 120 yards
length = 35 yards
You have information for two variables here. You have length and the parameter. So what should you do with them? Well, the question asks you to find the area. But to find the area you need to know the length as well as the width. But you only have the length.
To find the width you'll have to use the Parameter equation. You already know two variables that fit into it, Parameter and length. So let's plug them in:
120 yards = (2 * 35 yards) + (2 * width)
That should look familiar. It's a simple one-variable equation that you've seen a million times. That's the same as saying 120 = 70 + 2x. The "x" in this case is the width (which we need in order to solve for area). So we solve the equation for width!
First we simplify it:
120 yards = 70 yards + 2 * width
Next, we subtract 70 from bothsides:
50 yards = 2 * width
Finally, we divide both sides by two:
25 yards = width
Now we have our width! That's all we need to solve for area. Now we just plug everything into the Area equation:
Area = 35 yards * 25 yards
We solve for Area and we get:
Area = 875 yards * yards
Area = 875 yards^2 (yards squared)
There you go! Wasn't too hard, was it?