Question

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 6×2 − 16x. The width of the rectangular space is represented by the expression 2x.

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)

Part A: An expression to represent the length of the rectangular space is 6x² – 16x/ 2x
Part B: multiplying the length and the width of the rectangle is 6x² – 16x/ 2x × 2x

How to determine the expression

The formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
• l is the length
• w is the width
Now, substitute the expressions, we have;
6x² – 16x = 2x(l)
Make l, the length subject of formula by dividing both sides by its coefficient, we get;
Length, l = 6x² – 16x/ 2x
Now, let’s substitute both expressions for width and length
=  6x² – 16x/ 2x × 2x
Divide the common terms
=  6x² – 16x
Hence, the expression is  6x² – 16x/ 2x