1. **State the problem:** We are given an expression for the perimeter of a rectangle as $8w$, where $w$ is the width in inches. 2. **Recall the formula for the perimeter of a rectangle:** $$P = 2(\text{width} + \text{height}) = 2(w + h)$$ 3. **Set up the equation using the given expression:** $$8w = 2(w + h)$$ 4. **Solve for the height $h$ in terms of $w$:** $$8w = 2(w + h)$$ $$\Rightarrow \cancel{2}(4w) = \cancel{2}(w + h)$$ $$4w = w + h$$ $$h = 4w - w = 3w$$ 5. **Interpret the result:** The height $h$ is $3$ times the width $w$. 6. **Check the answer choices:** - The height of the rectangle is 4 times its width. (False) - The height of the rectangle is 3 times its width. (True) - The perimeter of the rectangle is 4 times its width. (False, perimeter is $8w$) - The perimeter of the rectangle is 3 times its height. (False) **Final answer:** The height of the rectangle is 3 times its width.