1. ## Geometry type question

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?

2. Hello, mcinnes!

Did you make a sketch?

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