1. **Problem Statement:** We have a mechanical jack shaped as a parallelogram with all four arms of equal length (a rhombus). The crank is 5 inches above the ground, and we want to find the height of the top of the jack. 2. **Key Properties:** In a rhombus, all sides are equal, and the diagonals are perpendicular and bisect each other. 3. **Assign variables:** Let the side length be $s$, and the diagonals be $d_1$ and $d_2$. The diagonals intersect at right angles and split each other into halves. 4. **Given:** The crank height is 5 inches, which corresponds to half of one diagonal, so: $$\frac{d_1}{2} = 5 \implies d_1 = 10$$ 5. **Relationship between side and diagonals:** Using the Pythagorean theorem in the right triangle formed by half diagonals: $$s = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2} = \frac{\sqrt{d_1^2 + d_2^2}}{2}$$ 6. **Find $d_2$ in terms of $s$ and $d_1$:** $$2s = \sqrt{d_1^2 + d_2^2} \implies (2s)^2 = d_1^2 + d_2^2 \implies d_2^2 = (2s)^2 - d_1^2$$ 7. **Height of the top of the jack:** The height corresponds to half of the other diagonal: $$\text{height} = \frac{d_2}{2} = \frac{\sqrt{(2s)^2 - d_1^2}}{2}$$ 8. **Since the crank is 5 inches above the ground, and the side length $s$ is the length of the arms, if $s$ is known, we can calculate the height. Without $s$, the height cannot be determined exactly.** **Summary:** The height of the top of the jack is $$\frac{\sqrt{4s^2 - d_1^2}}{2}$$ where $d_1=10$ inches and $s$ is the arm length. If the arm length $s$ is given, substitute to find the height. **Choice D is not necessarily correct without knowing $s$.**