Write and solve an equation for each situation.

Question

The perimeter of a parrellelogram is 72 meters. The width of the parrellelogram is 4 meters Less than its length. Find the length and width of the parrellelogram. 

Answer 1

The way to approach word problems is really just to write down in "math" language exactly what the problem says.

 

Always the first step is to choose a name for the variable -- usually the thing or things you are trying to figure out.  In this case, we want to know the length and the width.  Let's start by calling the length L and the width W.

 

First it says, "The perimeter of a parallelogram is 72 meters."  What's the perimeter of a parallelogra?  That's the sum of twice the length and twice the width.  So write that down:  2L + 2W = 72

 

Then:  "The width of the parallelogram is 4 meters less than its length."  That's simply W = L - 4.

 

So now you have 2 equations:

 

2L + 2W = 72

W = L - 4

 

I don't know if you've seen how to solve a system of two equations with two unknown, but if you haven't, it's pretty logical.  Since the second equation says W = L - 4, you can just replace W in the first equation with "L - 4".  You can do that kind of substitution any time two things are equal.

 

So that gives us:

 

2L + 2(L-4) = 72

 

Let's solve that:

 

2L + 2(L-4) = 72

2L + 2L - 8 = 72

4L - 8 = 72

4L = 80

L = 20

 

Now we know the length, and since the width is 4 less than the length, the width must be 16.

 

You can go back and make sure that this is correct by using this answer to find the perimeter:

 

P = 2L + 2W = 2*20 + 2*16 = 40 + 32 = 72

 

That's what they said in the problem, so the answer is correct.