Geometry type question

mcinnes · #1 $Old$ 11-18-2008, 09:54 AM

a rectangular garden measures 5mx4m its area is to be tripled by extending each dimension by the same amount. How much should each dimension extend?

Soroban · #2 $Old$ 11-18-2008, 10:54 AM

Hello, mcinnes!

Did you make a sketch?

Quote:

A rectangular garden measures 5m x 4m.
Its area is to be tripled by extending each dimension by the same amount.
How much should each dimension extend?

Code:

                            : - - x+5 - - :
                          - *-------------* -
                          x |             | :
    - *---------*         _ * - - - - *   | :
    : |         |         : |         |   | x+4
    4 |  20 m²  |         4 |         |   | : 
    : |         |         : |         |   | :
    - *---------*         - *---------*---* -
      :  - 5 -  :           :  - 5 -  : x :

The original garden is 5 by 4 and has an area of 20 m².

The new garden is $(x+5)$ by $(x+4)$ and has an area of 60 m².

There is our equation . . . . $(x+5)(x+4) \:=\:60 \quad\Rightarrow\quad x^2 + 9x - 40 \:=\:0$

Quadratic Formula: . $x \;=\;\frac{-9 \pm\sqrt{241}}{2}$

The positive root is: . $x \;=\;\frac{-9 + \sqrt{241}}{2} \;\approx\;3.262\text{ m}$