Answer:
3x² + 1
Step-by-step explanation:
The perimeter is the sum of the exterior lengths of a polygon.
Here, the perimeter will be the sum of the lengths of the triangle. Two of them are given: 5x² + x - 4 and 3x + 2. Let's say the third side is A. Then, we know that:
P = 8x² + 4x - 1 = (5x² + x - 4) + (3x + 2) + A
On the right side, we have:
(5x² + x - 4) + (3x + 2) + A
5x² + 4x - 2 + A
This is equal to 8x² + 4x - 1:
5x² + 4x - 2 + A = 8x² + 4x - 1
Solve for A by isolating it:
A = (8x² + 4x - 1) - (5x² + 4x - 2) = 8x² + 4x - 1 - 5x² - 4x + 2 = 3x² + 1
The third side is thus 3x² - 1.
