Question

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

Answer 1

Answer: $48a^4$

Step-by-step explanation:

 In this case we know that the  legs of the given right triangle have these lenghts:

$12a^4$ and $16a^4$

By definition, the sides of a right triangle are in the ratio $3:4:5$

Since:

$\frac{5}{4}=1.25$

We can multiply the lenght  $16a^4$ by 1.25 in order to find the lenght of the hypotenuse of the right triangle:

$(16a^4)(1.25)=20a^4$

Since the perimeter of a triangle is the sum of the lenghts of its sides, we can write the following expression for the perimeter of the given right triangle:

$12a^4+16a^4+20a^4$

Simplifying, we get:

$=48a^4$