Answer
$h=\dfrac{147}{5}$
Work Step by Step
Recall:
If $y$ varies directly as a power of $x$, then the direct variation's equation is $y=kx^n$ where $k$ is the constant of variation and $n$ is an integer.
Since $h$ varies directly as the square of $m$, then the equation of the direct variation, with $k$ as the constant of variation, is:
$$h=km^2$$
When $m=5$, $h=15$. Substitute these into the equation above to obtain:
\begin{align*}
h&=km^2\\\\
15&=k(5^2)\\\\
15&=25k\\\\
\frac{15}{25}&=k\\\\
\frac{3}{5}&=k
\end{align*}
Thus, the equation for the direct variation is:
$$a=\frac{3}{5}m^2$$
To find the value of $h$ when $m=7$, substitute $7$ to $m$ in the equation above to obtain:
\begin{align*}
h&=\frac{3}{5}m^2\\\\
h&=\frac{3}{5} \cdot (7^2)\\\\
h&=\frac{3}{5} \cdot 49\\\\
h&=\frac{147}{5}
\end{align*}
