Question

The following rectangle has an area of 3x^2-5x-12. What are the possible side lengths, in terms of x? Explain your answer and justify how you know that the sides you found are possible lengths

Answer 1

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

$3 {x}^{2} - 5x - 12$

1) write -5x as a difference

$3 {x}^{2} + 4x - 9x - 12$

2) factor out x from the expression 3x²+4x

$x(3x + 4) - 9x - 12$

3) factor out -3 from the expression -9x-12

$x(3x + 4) - 3(3x + 4)$

4) factor out 3x+4 from the expression

$(3x + 4)( x - 3)$

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

$length \times height$

(3x+4)(x-3)

= 3x²-9x+4x-12

= 3x²-5x-12 ( proven )