Question

1. A triangle has a perimeter of 8x^2 - xy + 4y^2 If two sides are known to be 2x^2 + 2xy and 4x^2 + 3y^2, then what expression represents the length of the third side? A. x^2 - 5xy + 3y^2B. 2x^2 -3xy + y^2C. -x^2 +5xy + 3y^2D. -2x^2 + 9xy + 4

Answer 1

we add up the two sides we have

$2x^2+2xy+4x^2+3y^2=6x^2+2xy+3y^{2^{}}$

then, the perimeter is the sum of all sides, therefore we subtract the above expression

$\begin{gathered} 8x^2-xy+4y^2-(6x^2+2xy+3y^2) \\ 8x^2-xy+4y^2-6x^2-2xy-3y^2 \\ 2x^2-3xy+y^2 \end{gathered}$

thats the expression, letter B