One side of a triangle is 2 cm shorter than the base, x. The other side is 3cm longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 46 cm?

Jan 13, 2016

$x \ge 15$

Explanation:

The base $= x$
Side1 $= x - 2$
Side2 $= x + 3$

The perimeter is the sum of the three sides.
$P = x + \left(x - 2\right) + \left(x + 3\right) \ge 46$
$3 x + 1 \ge 46$
$x \ge \frac{45}{3} = 15$