# Problem of the Day: 3/7/13

The area of a rectangle can be expressed as $3x^2-11x+6$. What is the perimeter of this rectangle in terms of $x$?

Solution to yesterday’s problem:

If the frog has an equal probability of landing on any lily pad, and he can land on two possible pads (he cannot jump vertically and land on the same lily pad), then the probability of him landing on a particular pad is $\frac{1}{2}$. Therefore, the probability of any permutation of three jumps is $\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}$.

Let’s make a tree diagram of all the possible ways he could jump. Say he started on lily pad 1. Here it is:

Notice that there are two ends of the branches that have a one, which is the pad the frog started on. So the probability of any of these two permutations occurring is $\frac{2}{8}$, or $\frac{1}{4}$.