Where do I begin? 'The length of a rectangle is....'

[jdruopp]

Please help me get an equation for this:

The length of a rectangle is 1cm longer than its width. If the diagonal of the rectangle is 4cm, what are the dimensions (length and width) of the rectangle?

 

[soroban]

Re: where do i begin

Hello, jdruopp!

Did you make a sketch?

The length of a rectangle is 1cm longer than its width.
If the diagonal of the rectangle is 4cm, what are the dimensions of the rectangle?

      * - - - - - - - - - - - *
      |                   *   |
      |          4   *        |
      |           *           | w
      |       *               |
      |   *                   |
      * - - - - - - - - - - - *
                w + 1

Let the width be \(\displaystyle w\).
Then the length is \(\displaystyle w\,+\,1\).

Look at the diagram . . . we have a right triangle.

Pythagorus tells us that; \(\displaystyle \:w^2\,+\,(w\,+\,1)^2\:=\:4^2\)

Can you finish it now?

 

[jdruopp]

So...

w^2 + w^2 +2w +1 =16
2w^2 +2w -15 = 0

Is this right so far?

 

[jonboy]

Yes you are correct. Now factor 2w^2 +2w -15 = 0.

 

[jdruopp]

ok, seems easy enough. But I still cant get it. Shouldn't the factors be 5 and 3?

(2w -5)(w+3) but that only gives 2w^2 +x -15 or the other gives 2w^2 -x -15

What am I doing wrong?

 

[skeeter]

nothing wrong ... except the stated quadratic will not factor.

 

[jdruopp]

Thank you, after trying for an hour I gave up.
So quadratic formula then?

 

[skeeter]

sounds like a plan.

 

[jdruopp]

Thanks a bunch, I figured it out. Hopefully the answer is right