# Problem of the Day: 12/22/12

Four consecutive integers have a sum of -118. What is the product of the first and last of these integers?

Solution to yesterday’s problem:
In the figure from yesterday, the triangle $UVW$ is a right triangle, and the hypotenuse is 13 units long. Knowing that 5-12-13 is a Pythagorean triple, we can deduce that $UV=12$ and $WV=5$. We’re also given the fact that the ratio $TU:UV=\frac{3}{2}$, so we can solve a proportion to find the length of side $TU$.
$\frac{l}{12}=\frac{3}{2}$
Cross multiplying,
$2l=36$
$l=18$
So the length of side TU is 18 units.