Question

write an expression in simplest form for the perimeter of a right triangle with leg lengths of 12a^4 and 16a^4an expression is____a^4

Answer 1

Given the lengths of the right triangle:

$\begin{gathered} 12a^4^{} \\ \text{and } \\ 16a^4 \end{gathered}$

To find the perimeter, use the formula:

$P=a+b+\sqrt[]{a^2+b^2}$

Thus, we have:

$P=12a^4+16a^4+\sqrt[]{(12a^4)^2+(16a^4)^2}$$\begin{gathered} P=28a^4+\sqrt[]{144a^4+256a^4} \\ P=28a^4+\sqrt[]{400a^4} \\ P=28a^4+20a^4 \\ P=48a^4 \end{gathered}$

Therefore, the expression is:

$48a^4$