Question

A triangle has sides measured `3x^2 +5x, 6x+7, and 9x^2- 2x -10`. How would you express the perimeter of this triangle as an equation?

Answer 1

The perimeter is `3(4x-1)(x+1)`

Explanation:

The perimeter of a triangle is the sum of its three sides.

as the three sides are `3x^2+5x`, `6x+7` and `9x^2-2x-10`

the perimeter is

`3x^2+5x+6x+7+9x^2-2x-10`

= `3x^2+9x^2+5x+6x-2x-10+7`

= `12x^2+9x-3`

This can be further factorized as follows

`12x^2+9x-3`

= `3(4x^2+3x-1)`

= `3(4x^2+4x-x-1)`

= `3(4x(x+1)-1(x+1))`

= `3(4x-1)(x+1)`