The plans for a shed call for a rectangular box with a perimeter of 264ft. The length is three times the width.

Question

find the length and width

Answer 1

To solve this problem you need to write equations and then solve the 'system' of equations.

If you look at the problem you will see there are at least 2 unknown things

(the Length and Width) so we will need two equations.

If more unknown things come up when we are working on the problem we will need more equations.

 

Lets call the length 'L' and the width 'W'

  - you can pick anything for the symbols but those are easy to remember.

 

Now lets look at the English sentences and see if we can translate those into our Maths language.

 

The length is three times the width.

L = 3 x W

 

...  rectangular box ... perimeter of 264 feet.

     I left out some English words that don't matter.

     Do you know the way to calculate the perimeter?  Add up all sides.

P = 264 ft  = L + W + L + W

     simplify this

P = 264 ft = (2 x L) + (2 x W)

     264 ft = 2L + 2W

 

There are different ways to solve systems of equations.

One way is to solve 1 equation to have 1 variable on one side = an expression of the other variable.

But one of our equations is already that way:  L = 3W

 

Now substitute that into the other equation and solve it.

L = 3W

264 ft = 2L + 2W  = 2(3W) +2W

I hope you see where this is going.

Find W.  Then use that to find L.

 

Comment to let us know how it goes, if you get stuck,

or if you want someone to check your answer.

Answer 2

let w=width

let 3w=length(length is 3 times the width)

P=2l+2w (formula for perimeter of a rectangle)

264=2(3w)+2w

264=6w+2w

264=8w

264/8=w

33 ft=w

3(33)=99 ft=l

check:

264=2(99)+2(33)

264=198+66

264=264