What is the answer to this question? Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 3a to the third power and 4a to the third power.

Step-by-step explanation:

Since the length of both legs of the right angle triangle are given, we would determine the hypotenuse, h by applying Pythagoras theorem which is expressed as

Hypotenuse² = one leg² + other leg²

Therefore,

h² = (3a) ³ + (4a) ³

h² = 27a³ + 64a³

h² = 91a³

Taking square root of both sides,

h = √91a³

The formula for determining the perimeter of a triangle is expressed as

Perimeter = a + b + c

a, b and c are the side length of the triangle. Therefore, the expression for the perimeter of the right angle triangle is

√91a³ + (3a) ³ + (4a) ³

= √91a³ + 91a³