Question

all four arms of a mechanical jack are the same length, and they form a parallelogram. turning the crank pulls the arms together, raising the top of the jack. how high is the top of the jack when the crank is 5 inches off the ground? explain. select the correct choice below, and fill in the answer box to complete your choice. (type an integer or a decimal.) a. the height of the top of the jack is \\(\square\\) inches because opposite sides of a parallelogram are congruent. b. the height of the top of the jack is \\(\square\\) inches because opposite sides of a parallelogram are parallel. c. the height of the top of the jack is \\(\square\\) inches because the diagonals of a parallelogram are perpendicular to each other. d. the height of the top of the jack is \\(\square\\) inches because the diagonals of a parallelogram bisect each other.

Explanation:

Step1: Recall Parallelogram Diagonals Property

In a parallelogram, the diagonals bisect each other. The mechanical jack has arms forming a parallelogram, and the crank's height (5 inches) relates to half the diagonal? Wait, no—wait, the key here is that when the crank is 5 inches off the ground, the top's height: since diagonals bisect each other, the total height would be twice? Wait, no, let's think again. The jack's structure: the vertical line (the diagonal) is split by the midpoint (since diagonals bisect each other). So if the crank is 5 inches off the ground, the top's height is 10? Wait, no, wait the options: option D says diagonals bisect each other. So the height from ground to crank is 5, and since diagonals bisect, the top is 5*2=10? Wait, no, maybe the crank is at the midpoint. Wait, the problem: all four arms are same length, form a parallelogram. Turning crank pulls arms together, raising top. When crank is 5 inches off ground, how high is top?

Wait, the diagonals of a parallelogram bisect each other. So the distance from ground to crank is half the total height (from ground to top). So if crank is 5 inches, top is 10? Wait, no, maybe the crank is at the midpoint, so the height from ground to crank is 5, and from crank to top is also 5, so total 10? Wait, but let's check the options. Option D: "The height of the top of the jack is [ ] inches because the diagonals of a parallelogram bisect each other." So if the crank is at the midpoint (since diagonals bisect), then the height from ground to crank is 5, so from ground to top is 5*2=10? Wait, no, maybe the crank is 5 inches, so the top is 10? Wait, maybe I got it wrong. Wait, the crank is 5 inches off the ground, and since diagonals bisect, the top is 10? Wait, no, maybe the height is 10? Wait, let's re-express.

Step2: Apply Diagonals Bisect Property

In a parallelogram, diagonals bisect each other. So the segment from ground to crank is one part of a diagonal, and from crank to top is the other part, which are equal (since diagonals bisect). So if crank is 5 inches off ground, then top is 5 + 5 = 10 inches? Wait, no, maybe the crank is at the midpoint, so the distance from ground to crank is 5, so from ground to top is 10. So the correct option is D, with height 10.

Answer:

D. The height of the top of the jack is 10 inches because the diagonals of a parallelogram bisect each other.