Question

The perimeter, in units, of the triangle is 12x^2 + 8x - 6.What is the length, in units, of the third side?

Answer 1

Step 1: Write out the formula for finding the perimeter of a triangle

`p=a+y+z`
`\begin{gathered} \text{ Where} \\ p=\text{ the perimeter of a triangle} \\ a,y,\text{ and }z\text{ are the thre}e\text{ sides of the triangle} \end{gathered}`

Step 2: Write out the given values and substitute them into the formula

`p=12x^2+8x-6,a=3x^2-5x,y=7x^2+8,z=?`

Therefore,

`\begin{gathered} z+3x^2-5x+7x^2+8=12x^2+8x-6 \\ z+3x^2+7x^2-5x+8=12x^2+8x-6 \\ z+10x^2-5x+8=12x^2+8x-6 \\ \text{hence} \\ z=12x^2-10x^2+8x+5x-6-8 \\ z=2x^2+13x-14 \end{gathered}`

Hence the