Question

the diagram shows the lengths, in units, of two sides of a triangle. not drawn to scale the perimeter, in units, of the triangle is 12x^2 + 8x - 6. what is the length, in units, of the third side? a. 22x^2 + 3x + 2 b. 22x^2 + 11x - 6 c. 2x^2 + 5x + 2 d. 2x^2 + 13x - 14

Explanation:

Step1: Recall perimeter formula

Let the sides be $a = 7x^{2}+8$, $b = 3x^{2}-5x$, and perimeter $P=12x^{2}+8x - 6$. The formula for the perimeter of a triangle is $P=a + b + c$. So, $c=P-(a + b)$.

Step2: Calculate $a + b$

$a + b=(7x^{2}+8)+(3x^{2}-5x)=7x^{2}+3x^{2}-5x + 8=10x^{2}-5x + 8$.

Step3: Calculate the third - side $c$

$c=(12x^{2}+8x - 6)-(10x^{2}-5x + 8)$
$=12x^{2}+8x - 6-10x^{2}+5x - 8$
$=(12x^{2}-10x^{2})+(8x + 5x)+(-6 - 8)$
$=2x^{2}+13x-14$.

Answer:

D. $2x^{2}+13x - 14$