Gallery Problems Exercise

Equations about Figures

Work Time

Equations about Figures

  1. A rectangle is 8 feet long and 6 feet wide. If each dimension is increased by the same number of feet, the area of the new rectangle is 80 square feet. Write an equation for the new rectangle, with x representing the increase in feet.
  2. Here is an equation stating that the area of the shaded region is 260 square centimeters:

    8a(3a – 2) – 3a(a + 1) = 260

    Confirm that a = 4 is the solution to this equation.

  3. Marcus said, “If the area of the smaller, white rectangle in the figure is 246 square centimeters, a would have to equal –3.”
    • Does this solution make sense? Why or why not?
    • What would the dimensions of both rectangles in the figure be if a were equal to –3?
  4. A piece of wire 36 centimeters long is bent into the shape of a rectangle with a length that is twice its width. Write an equation for the width.