Translate the following into a quadratic equation, and solve it:
The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what are its dimensions?
You are supposed to know that the area of a rectangle is calculated by:
$\displaystyle A=l \cdot w~,~w,l \geq 0$
You know that $\displaystyle l = 3w$ . Plug in this term instead of l into the formula and you get:
$\displaystyle a = 3w \cdot w = 75$ . Therefore:
$\displaystyle 3w^2 = 75~\iff~w^2 = 25~\iff~ w = 5$
So the dimensions of the rectangle are l = 15 and w = 5