Calculate Rectangle Perimeter: Finding the Distance Around a 6 by 10 Shape

Let's solve for the perimeter of the rectangle by following these steps:

• First, identify the given information: The diagonal $AC$ is 10 units and the height $BC$ is 6 units.
• Next, use the Pythagorean theorem to calculate the missing side (the base), $AB$. Given that $AB^2 + BC^2 = AC^2$, we can write:
• Step 1: Substitute known values into the equation: $AB^2 + 6^2 = 10^2$.
• Step 2: Calculate $AB^2$:
$AB^2 + 36 = 100\\ AB^2 = 100 - 36\\ AB^2 = 64\\ AB = \sqrt{64} = 8$

We have found the base $AB = 8$ units.

Now, calculate the perimeter $P$ using the perimeter formula $P = 2(l + w)$, where $l$ is the length (AB = 8) and $w$ is the width (BC = 6).

Therefore, the perimeter of the rectangle is 28 units.

The correct choice is 3: 28.