Word problem

Question

A rectangular sandbox is surrounded on all sides by a strip of grass that is 5 feet wide on all sizes. The length of the sandbox is 4 feet more than the width and the total area for the sandbox and the grass is 190 square feet. find the dimensions of the sandbox 

Answer 1

Hi Corrina,

If we say L=length and W=width, we know:

L=W+4

 

If A is the total area, we also know:

A=190ft²

 

Now, if we recall that area=length*width, we can say:

A=(L+10)*(W+10)

(note that we had to add 10 to both the length and width because of the grass on both sides of the sandbox - ie. 5+5)

 

Going back to our first equation, we can substitute W+4 in for L into our third equation, and 190 for A.

190=(W+4+10)*(W+10)

 

Solve for W to find the width of the sandbox, and then add 4 to find the length.