#### Answer

The trinomial $x^{2}-24x+c$ is a perfect square when $c=144.$
Then $x^{2}-24x+144=(x-12)(x-12)=(x-12)^{2}$

#### Work Step by Step

$ x^{2}-24x+c\qquad$ ... find half the coefficient of $x$, which is $\displaystyle \frac{-24}{2}=-12$.
$\qquad$ ...square the result.
$(-12^{2})=144\qquad$ ...substitute $c$ with $144$ in the original expression
$x^{2}-24x+144=(x-12)^{2}$