Answer
$C(h)\:=\;5h(\sqrt{2}+2)$
Work Step by Step
The perimeter of the given isosceles right triangle with equal sides measuring $\:x\:$ and hypotenuse $\:h\:$ is $\:2x+h.$
Apply the pythagorean theorem to get the length of equal sides in terms of $\:h.$
$x^2+x^2=h^2$
$\Rightarrow\: x=\frac{h}{\sqrt{2}}=\frac{h\sqrt{2}}{2}$
So, the perimeter of the triangle becomes:
$=\:2\cdot(\frac{h\sqrt{2}}{2})+h=h\sqrt{2}+h$
The function for the cost of fencing would be:
$C=5\cdot h\sqrt{2}+10\cdot h$
$C=5h(\sqrt{2}+2)$
