Answer:
the possible side lengths:
3x+4 and x-3
Step-by-step explanation:
factorize the the expression and you will get two expressions in terms of x. those expressions are the lengths of the rectangle
[tex]3 {x}^{2} - 5x - 12[/tex]
1) write -5x as a difference
[tex]3 {x}^{2} + 4x - 9x - 12[/tex]
2) factor out x from the expression 3x²+4x
[tex]x(3x + 4) - 9x - 12[/tex]
3) factor out -3 from the expression -9x-12
[tex]x(3x + 4) - 3(3x + 4)[/tex]
4) factor out 3x+4 from the expression
[tex](3x + 4)( x - 3)[/tex]
the possible lengths are 3x+4 and x-3
to check whether the answer is correct, you can just multiply the both lengths using the area of rectangle formulae
area of rectangle formulae
[tex]length \times height[/tex]
(3x+4)(x-3)
= 3x²-9x+4x-12
= 3x²-5x-12 ( proven )
