H.O.T. Problems Higher Order Thinking 9. CESS Use Math Tools Draw a rectangle on a coordinate plane that has a perimeter of 16 units. Label all of the vertices with the coordinates. Then find the area of the rectangle.

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1. Let the lengths of the rectangle be $$ x $$ and $$ y $$. The perimeter $$ P $$ is given by
   $$
   P = 2(x + y)
   $$
   Since the perimeter is 16 units, we have
   $$
   2(x+y) = 16 \quad \Longrightarrow \quad x+y=8.
   $$

2. One simple choice is to let $$ x=3 $$ and $$ y=5 $$ since
   $$
   3+5=8.
   $$
   (There are many possible pairs $$(x,y)$$ that satisfy $$ x+y=8 $$; this is just one convenient option.)

3. To draw the rectangle on the coordinate plane, choose one vertex at the origin. Place the rectangle so its sides are parallel to the axes. Define the vertices as follows:
   - $$ A=(0,0) $$
   - $$ B=(3,0) $$ (moving 3 units along the $$x$$-axis)
   - $$ C=(3,5) $$ (moving 5 units up from $$ B $$)
   - $$ D=(0,5) $$ (moving left from $$ C $$ back to the $$ y $$-axis)

4. Check the perimeter using these coordinates:
   - Side $$ AB $$ has length $$ 3 $$.
   - Side $$ BC $$ has length $$ 5 $$.
   - Side $$ CD $$ has length $$ 3 $$.
   - Side $$ DA $$ has length $$ 5 $$.
   
   The total perimeter is
   $$
   3+5+3+5=16 \text{ units},
   $$
   which meets the requirement.

5. Next, find the area of the rectangle. The area $$ A $$ is calculated as
   $$
   A = x \times y = 3 \times 5 = 15.
   $$

Thus, the area of the rectangle is $$ 15 $$ square units.
To create a rectangle with a perimeter of 16 units, you can choose sides of length 3 and 5 units. Plotting the rectangle on a coordinate plane with vertices at (0,0), (3,0), (3,5), and (0,5), the area is 15 square units.

H.O.T. Problems Higher Order Thinking 9. CESS Use Math Tools Draw a rectangle on a coordinate plane that has a perimeter of 16 units. Label all of the vertices with the coordinates. Then find the area of the rectangle.

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