A rectangular field has a perimeter of 200 yards. The length of the field is 10 yards longer than twice the width. What are the dimensions of the field?

Question

A rectangular field has a perimeter of 200 yards. The length of the field is 10 yards longer than twice the width. What are the dimensions of the field?

Answer 1

Hi Hannah,

I remember how confusing these problems can be when you are first learning them.  Let's see if I can help you make sense of this one . . .

 

The first thing we are told is that the perimeter of the rectangle is 200 yards.  

If L is the length and W is the width, then we know that 2L + 2W = 200.  

 

Sometimes it can be easier to consider just half the perimeter.  

This means that the L + W = 100.   Call this Equation 1 and save it for later!

 

Now, lets look at the next sentence:

The length of the field is 10 yards longer than twice the width.  

 

Convert this sentence into math symbols:

[The length of the field] [is] [10 yards longer than] [twice the width]

L = 10 + 2W

 

Since L is the same as 10+2W, substitute that into Equation 1.

 

Remember, equation 1 said that L + W = 100

so, that means that (10 + 2W) + W = 100 since the 10+2W replaced the L

 

10 + 2W + W = 100

10 + 3W = 100

3W = 90

W = 30

 

and if W is 30, then what is L?

L + W = 100

L + 30 = 100

L = 70

 

So, the field is 70 by 30!!

 

Hope this helps!!  Keep practicing!!