Find and simplify the perimeter of a right triangle.

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?

Answer 1

While I usually do not respond to a question another tutor has already answered, I think there is an easier way to solve this problem.

 

The hypotenuse of this 3-4-5 triangle is 5a to the third power (as you have written it).

 

The perimeter is the sum of 3a to the third power + 4a to the third power + 5a to the third power.

 

As the first tutor suggested it is difficult to be sure what you meant by 3a to the third power etc; therefore, I have just used your notation.

Answer 2

a² + b² = c²

[(3a)³]²  + [(4a)³]² = c²   I'm assuming the length was (3a)³, not 3a³. It was difficult to tell in your question.

(3a)⁶ + (4a)⁶ = c²

729a⁶ + 4096a⁶ = c²

4825a⁶ = c²      Take the square root of both sides.

69.4622a³ ≈ c