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You have a rectangular space where you plan to create an obstacle course for an animal. The area of the rectangular space is represented by the expression 12x2 − 15x. The width of the rectangular space is represented by the expression 3x.

Part A: Write an expression to represent the length of the rectangular space. Then simplify your expression. Show all your work. (6 points)

Part B: Prove that your answer in part A is correct by multiplying the length and the width of the rectangle. Show all your work. (4 points)

Sagot :

semsee45

Answer:

[tex]\textsf{A)} \quad \ell = \dfrac{12x^2-15x}{3x}=4x-5[/tex]

B)  Proof given below.

Step-by-step explanation:

Given values:

[tex]\textsf{Area}=12x^2-15x[/tex]

[tex]\textsf{Width} = 3x[/tex]

Area of a rectangle

[tex]A=w \cdot \ell[/tex]

where:

  • [tex]w[/tex] = width
  • [tex]\ell[/tex] = length

Part A

Substitute the given values into the area formula and solve for length:

[tex]\begin{aligned} A & = w \cdot \ell\\ \implies 12x^2-15x & = 3x \cdot \ell\\\ell & = \dfrac{12x^2-15x}{3x}\\\ell & = \dfrac{3x(4x-5)}{3x}\\\ell & = 4x-5\end{aligned}[/tex]

Part B

Prove by multiplying the given width by the found length:

[tex]\begin{aligned}A & = w \cdot \ell\\ \implies A & = 3x(4x-5)\\& = 3x \cdot 4x - 3x \cdot 5\\& = 12x^2-15x\end{aligned}[/tex]

Hence proving that the length of the rectangle is (4x - 5).

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