Answer: [tex]48a^4[/tex]
Step-by-step explanation:
In this case we know that the legs of the given right triangle have these lenghts:
[tex]12a^4[/tex] and [tex]16a^4[/tex]
By definition, the sides of a right triangle are in the ratio [tex]3:4:5[/tex]
Since:
[tex]\frac{5}{4}=1.25[/tex]
We can multiply the lenght [tex]16a^4[/tex] by 1.25 in order to find the lenght of the hypotenuse of the right triangle:
[tex](16a^4)(1.25)=20a^4[/tex]
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:
[tex]12a^4+16a^4+20a^4[/tex]
Simplifying, we get:
[tex]=48a^4[/tex]
The expression in the simplest form that represents the perimeter of the right triangle with legs 12a⁴ and 16a⁴ is 48a⁴
A right angle triangle has one of its angles as 90 degrees. The sides can be found using pythagoras theorem.
Therefore,
The perimeter of the right triangle is the sum of the whole sides. Therefore, let's find the hyotenuse.
c² = a² + b²
c² = (12a⁴)² + (16a⁴)²
c² = 144a⁸ + 256a⁸
c² = 400a⁸
c = √400a⁸
c = 20a⁴
Therefore, the perimeter is as follows:
perimeter = 12a⁴ + 16a⁴ + 20a⁴
perimeter = 48a⁴
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