Question

Question 4: You are creating an obstacle for a community event. The area of the rectangular space is represented by the expression 8x² - 12x. The width of the rectangular space is represented by the expression 4x.

Part A: Write an expression to represent the length of the rectangular space. Show all work to find the length

Length of Rectangular Space

Part B: Prove your answer from Part A is correct by multiplying the length and width of the rectangle.

Write the expression in standard form:​

Answer 1

Part A: To find the expression for the length of the rectangular space, we can use the formula for the area of a rectangle, which is length multiplied by width. We have the expression for the area as 8x² - 12x, and the expression for the width as 4x. So, we can write:

Area = Length × Width

8x² - 12x = Length × 4x

Simplifying the right side by multiplying, we get:

8x² - 12x = 4x × Length

2x² - 3x = Length

Therefore, the expression for the length of the rectangular space is 2x² - 3x.

Part B: To prove that the expression for the length from Part A is correct, we can multiply it by the expression for the width and simplify:

Length × Width = (2x² - 3x) × (4x)

= 8x³ - 12x²

= 4x(2x² - 3x)

= 4x(2x(x - 3))

This is in fact the same as the expression for the area of the rectangular space, 8x² - 12x, in standard form.