Answers

1. Answer:

   the expression for the width is 4x + 3

   Step-by-step explanation:

   Area = base times width.  Thus, we divide 9x – 2 into 36x^2 + 19x – 6 to find an expression for the width.  Dividing 9x into 36x^2, we get 4x, which tells us that the first term of the quotient starts with 4x:    (4x + ? )(9x – 2).  Replacing the ‘?’ with 3, we get:

   (4x + 3)(9x – 2), which through multiplication becomess

   36x^2 + 27x – 8x – 6, or 36x^2 + 19x – 6, which was the original dividend.

   Thus the expression for the width is 4x + 3 (in meters).

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2. Answer:

   The area of the floor plan is given by the expression 20x² – 4x – 16

   A rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are parallel and equal to each other. Also all the angles of a rectangle measure 90 degrees each.

   Area of a rectangle = length * breadth

   Area of the floor plan = length * breadth

   Area of the floor plan = (5x + 4) * (4x – 4)

   Area of the floor plan = 20x² – 20x + 16x – 16

   Area of the floor plan = 20x² – 4x – 16

   The area of the floor plan is given by the expression 20x² – 4x – 16.

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