Answer:
106.4622 [tex]a^{3}[/tex]
Step-by-step explanation:
Given the information:
Use the pytagon theory to find the hypotenuse of the triangle
[tex]a^{2} + b^{2} = c^{2}[/tex]
<=>[tex]((3a)^{3}) ^{2} + ((4a)^{3}) ^{2} = c^{2}[/tex]
<=>[tex](3a)^{6} + (4a)^{6} = c^{2}[/tex]
<=> [tex]c^{2} = 4285a^{6}[/tex]
Take the square root of both sides
<=> c = 69.4622 [tex]a^{3}[/tex]
=> expression in simplest form for the perimeter of a right triangle is:
[tex](3a)^{3}[/tex] + [tex](4a)^{3}[/tex] + 69.4622 [tex]a^{3}[/tex]
= 27[tex]a^{3}[/tex] + 64[tex]a^{3}[/tex] + 69.4622 [tex]a^{3}[/tex]
= 106.4622 [tex]a^{3}[/tex]
