Questions: Three vertices of a rectangle are shown. What is the perimeter of the rectangle? Enter your answer in the box. units

Transcript text: Three vertices of a rectangle are shown. What is the perimeter of the rectangle? Enter your answer in the box. $\square$ units

Solution

Solution Steps

Step 1: Identify the given vertices

The given vertices of the rectangle are:

(7, 6)
(3, 5)
(3, -6)

Step 2: Determine the missing vertex

To form a rectangle, the missing vertex must align with the given vertices. The missing vertex should be (7, -6).

Step 3: Calculate the lengths of the sides

The length of the vertical side is the difference in the y-coordinates of (7, 6) and (7, -6), which is |6 - (-6)| = 12 units.
The length of the horizontal side is the difference in the x-coordinates of (7, 6) and (3, 6), which is |7 - 3| = 4 units.

Step 4: Calculate the perimeter

The perimeter of a rectangle is given by the formula: \[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \] Substituting the values: \[ \text{Perimeter} = 2 \times (12 + 4) = 2 \times 16 = 32 \text{ units} \]