If an equithagorean triangle is an equilateral triangle in which the sum of the cubes of two sides is equal to the square of the third side, what is the perimeter of an equithagorean triangle?

A. 0.5
B. 1.5
C. 4.5
D. 6

Of course all sides are the same

let the side be x

given: "the sum of the cubes of two sides is equal to the square of the third side"
... just translate into math

2x^3 = x^2
2x^3 - x^2 = 0
x^2(2x - 1) = 0
x = 0 , which would make an interesting triangle
or
x = 1/2
So the perimeter is 3x = 3/2, which is your choice B

What is an "equithagorean triangle?"

Yup, this question is weird. They say its a equilateral triangle when the sum of the cubes of the two sides are equal to the square of the third...

To find the perimeter of an equithagorean triangle, we first need to understand the properties of such a triangle.

Let's assume the sides of the equithagorean triangle are a, b, and c. According to the definition, the triangle is equilateral, so all sides are equal: a = b = c.

The equation for the equithagorean triangle states that the sum of the cubes of two sides (a and b) is equal to the square of the third side (c):

a³ + b³ = c²

Since all sides are equal, we can simplify the equation to:

2a³ = c²

Now, we can find the perimeter by summing all three sides:

Perimeter = a + b + c

Since a = b = c, we can substitute c with a:

Perimeter = a + a + a

Perimeter = 3a

We need to find the value of a in the equation 2a³ = c², and then multiply it by 3 to get the perimeter.

To find the value of a, we can rearrange the equation:

2a³ = c²
a³ = c² / 2
a = ∛(c² / 2)

Now, let's substitute this value of a into the Perimeter equation:

Perimeter = 3 * ∛(c² / 2)

To determine the correct answer among the provided options (A. 0.5, B. 1.5, C. 4.5, D. 6), we need to know the value of c². Without a specific value for c², we cannot determine the exact answer.

However, we can conclude that the perimeter of an equithagorean triangle is proportional to the cube root of c² divided by 2.