[email protected] wrote:Given line L (illustrated in graph), and a parallel line that runs through (-1,5), what is the perimeter of a rectangle whose sides run along the two lines and has a length of 9?

28
9√15
18 + 2√20
36
45

We can plug in the answers, which represent the perimeter of the rectangle.
The correct answer is almost certain to be an integer value (A, D, or E).

It is given that two sides of the rectangle each have a length of 9, yielding a sum of 18.
If we subtract 18 from the values in A, D and E, we get the following options for the OTHER two sides of the rectangle:

A: 28-18 = 10, implying that the other two sides each have a length of 5.
D: 36-18 = 18, implying that the other two sides each have a length of 9.
E: 45-18 = 27, implying that the other two sides here each have a length of 13.5.

D implies that the rectangle is a square.
E yields a non-integer value.
Thus, the correct answer is probably A.

Answer choice A: p = 28.
If the perimeter of the rectangle is 28, then the rectangle has a length of 9 and a width of 5.
A width of 5 should make us look for a 3-4-5 triangle:


If ∆ABC is in fact a 3-4-5 triangle, then the coordinates of point C must be (2,1).
Confirm that (2,1) is on the line defined by y = (3/4)x - 1/2:
1 = (3/4) * 2 - 1/2
1 = 3/2 - 1/2
1 = 1.
Success!
Since ∆ABC is a 3-4-5 triangle, the dimensions of the rectangle must be as shown in the figure above.

The correct answer is A.