Answered

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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

Sagot :

rebeccarayshma

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 )

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