Answer
$c=9$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the concepts of the square of a binomial to find the missing term.
$\bf{\text{Solution Details:}}$
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ then the last term, $b^2,$ is equal to
\begin{array}{l}\require{cancel}
\left(\dfrac{2ab}{2a} \right)^2
.\end{array}
Hence, in the given perfect square trinomial, $
100r^2-60r+c
,$ where $a=10$ and $2ab=-60$, the last term, $c,$ is equal to
\begin{array}{l}\require{cancel}
\left(\dfrac{-60}{2(10)} \right)^2
\\\\=
\left(\dfrac{-60}{20} \right)^2
\\\\=
\left(-3\right)^2
\\\\=
9
.\end{array}
Hence, $
c=9
.$
