Question

Find the perimeter of a triangle. Simplify your answer
Side A: 2y^2-2x^2
Side B: 5x^2-2y^2-21
Base: y^2-x^2+11

Answer 1

To find the perimeter of a triangle, we need to sum the lengths of all its sides. The sides of the triangle are given as:

- Side A: \( 2y^2 - 2x^2 \)
- Side B: \( 5x^2 - 2y^2 - 21 \)
- Base: \( y^2 - x^2 + 11 \)

The perimeter \( P \) can be calculated as follows:

\[
P = \text{Side A} + \text{Side B} + \text{Base}
\]

Substituting the values of the sides:

\[
P = (2y^2 - 2x^2) + (5x^2 - 2y^2 - 21) + (y^2 - x^2 + 11)
\]

Now, we will combine like terms:

1. Combine the \( y^2 \) terms:
- \( 2y^2 - 2y^2 + y^2 = 0y^2 + y^2 = y^2 \)

2. Combine the \( x^2 \) terms:
- \( -2x^2 + 5x^2 - x^2 = (5 - 2 - 1)x^2 = 2x^2 \)

3. Combine the constant terms:
- \( -21 + 11 = -10 \)

Putting it all together:

\[
P = y^2 + 2x^2 - 10
\]

Thus, the perimeter of the triangle is:

\[
\boxed{y^2 + 2x^2 - 10}
\]