Solve the equation

Question

A man has 40 ft. of fencing to put around a rectangular garden. If the length is 4 times the width, find the dimensions of his garden.
length    ft
width     ft

Answer 1

I'll give this a go: What information is given to you? 

 

-You know that the fence is 40ft, so we can infer that the perimeter of the garden is also 40ft.

 

-The formula for perimeter of a rectangle is 2(length)+2(width)=P 

 

- Since P is given, we'll rewrite this

as: 2(length)+2(width)=40ft

 

The length of your garden is 4 times as long as your width. But you don't have a value for your width. This is where you may need to substitute this missing value with x. 

 

Since we know our width is now x, we can rewrite the perimeter formula

as: 2(length)+2(x)=40ft

 

Now we still need our lengths. 

If the length is 4 times as much as the width, then we can write it as being 4 times x. 

 

You're left with the equation

2(4x)+2(x)=40ft

which becomes 8x+2x=40ft

 

Solve for x and plug that back into the original question. 

Don't forget to show your units.