1. **Problem Statement:** We have a mechanical jack shaped as a parallelogram with all four arms of equal length. The crank is 5 inches above the ground, and we want to find the height of the top of the jack. 2. **Key Properties of a Parallelogram:** - Opposite sides are parallel and congruent. - Diagonals bisect each other. - Diagonals are not necessarily perpendicular. 3. **Understanding the Setup:** Since all arms are equal, the parallelogram is actually a rhombus. In a rhombus, the diagonals are perpendicular and bisect each other. 4. **Using the Diagonals:** The crank height corresponds to one diagonal's half-length (5 inches). Let the diagonals be $d_1$ and $d_2$. Since the crank is 5 inches off the ground, half of one diagonal is 5 inches, so $\frac{d_1}{2} = 5$ which means $d_1 = 10$ inches. 5. **Finding the Height (other diagonal half):** The height of the top of the jack corresponds to the other diagonal's half-length. Since the arms are equal, the sides satisfy the rhombus property: $$\text{side} = \frac{\sqrt{d_1^2 + d_2^2}}{2}$$ 6. **Since all arms are equal, the side length is constant.** If the crank is 5 inches off the ground, the height of the top is the same 5 inches because the diagonals are perpendicular and bisect each other. 7. **Answer:** The height of the top of the jack is 5 inches because the diagonals of a parallelogram are perpendicular to each other. **Choice D is correct.**