Question

Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 3a cubed and 4a cubed

Answer 1

Answer:

106.4622 $a^{3}$

Step-by-step explanation:

Given the information:

• A right triangle

• Leg lengths of $(3a)^{3}$ and $(4a)^{3}$

Use the pytagon theory to find the hypotenuse of the triangle

$a^{2} + b^{2} = c^{2}$

<=>$((3a)^{3}) ^{2} + ((4a)^{3}) ^{2} = c^{2}$

<=>$(3a)^{6} + (4a)^{6} = c^{2}$  

<=> $c^{2} = 4285a^{6}$

Take the square root of both sides

<=> c = 69.4622 $a^{3}$

=> expression in simplest form for the perimeter of a right triangle is:

$(3a)^{3}$ + $(4a)^{3}$ + 69.4622 $a^{3}$  

= 27$a^{3}$  + 64$a^{3}$  + 69.4622 $a^{3}$  

= 106.4622 $a^{3}$