Help on a basic Math B Regents Problem

[Dark Knight 496]

I am unable to solve the following problem from a June 2001 math b regents:

A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet, but building code laws state that a homeowner cannot have a deck larger than 900 square feet. If the length and the width are to be increased by the same amount, find, to the nearest tenth, the maximum number of feet that the length of the deck may be increased in size legally.

Please help, thanks.

 

[soroban]

Hello, Dark Knight 496!

Did you make a sketch?

A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet,
but building code laws state that a homeowner cannot have a deck larger than 900 square feet.
If the length and the width are to be increased by the same amount, find, to the nearest tenth,
the maximum number of feet that the length of the deck may be increased in size legally.

      :   20    :   x   :
    - *---------* - - - *  -
      |         |       :
   15 |         |       :
      |         |       :
    - *---------*       : 15+x
      :                 :
    x :                 :
      :                 :
    - * - - - - - - - - *  -
      :      20+x       :

The original deck has dimensions 20 by 15 feet.

The length and width are increased by a uniform amount, \(\displaystyle x\) feet.

The new length is \(\displaystyle 20\,+\,x\); the new width is \(\displaystyle 15\,+\,x\).

The new area is: .\(\displaystyle L\,\times\,W \;=\;(20\,+\,x)(15\,+\,x)\)

This area must not exceed 900 square feet.

To have exactly 900 square feet: \(\displaystyle \,(20 + x)(15 + x)\;=\;900\)

Can you finish it now?

 

[Dark Knight 496]

Yup, it's simple, I just for some reason stumbled over it and didn't know how to start. It's 12.6. Thanks a lot.