The sides of a trapezoid are 5, 8, 11, and 13, and its diagonals are also integer numbers; what are they?
I also wrote a program testing all cases using the law of cosines. I similarly found no match.
Here's a summary of my program:
-Let a,b,c,d be the sides of the trapezoid, with a and c being the parallel sides. For each possible assignment of these variables:
-Compute the quantity q=ab^2+ac^2+cb^2+ca^2.
-Let x and y independently range from 1 to floor(sqrt(q)). These will represent the diagonals. For each assignment of x and y:
-Compute the quanity p=ax^2+cy^2.
-If p equals q, print as a candidate solution.
No candidate solutions were printed.
The equation p=q must follow from the following derivation:
x^2 = b^2 + c^2 - 2bc*cos(theta)
y^2 = b^2 + a^2 +2ab*cos(theta)
(using the fact that the angles surrounding side b are theta and 180-theta)
Multiply the first equation by a, the second by c, and add, to get:
p=q.
Another failed attempt
