Car jacks are constructed like a rhombus. When used to raise a car, the rhombus is seen. If the sides of the rhombus are 13 inches, what is the maximum lenght of the shaft
depends on the mininum the screw can retract. Theoretically, it is zero, so max height is 26inches, at which the rhombus is a line upward, very unstable.
To find the maximum length of the shaft, we can use the properties of a rhombus. In a rhombus, opposite sides are equal in length, but the diagonals are not necessarily equal.
In this case, we know that the sides of the rhombus (the car jack) are 13 inches. Since the rhombus is being used to raise a car, the diagonals of the rhombus will appear.
The diagonal of a rhombus is the line segment that connects the opposite vertices. There are two diagonals in a rhombus - one longer diagonal and one shorter diagonal.
To find the length of the longer diagonal, we can use the Pythagorean theorem. Let's call the longer diagonal "d".
Based on the properties of a rhombus, the diagonals divide the rhombus into four congruent right triangles. In this case, the sides of the rhombus are given as 13 inches, so the sides of each right triangle would be half of that length, which is 6.5 inches.
Using the Pythagorean theorem:
d^2 = (6.5)^2 + (6.5)^2
d^2 = 42.25 + 42.25
d^2 = 84.5
d ≈ 9.19 inches (rounded to two decimal places)
Therefore, the maximum length of the shaft is approximately 9.19 inches.