Triangle EFG is a right angled triangle (right angled at ∠EGF) with EG = 7, FG = 24.

Point P is the midpoint of EF, and:

H is on the same side of line EF as G so that EH = FH = 15, and:

The area of triangle GHP is expressible as x*√y/z, where each of x, y and z is a positive integer, and:

x and z are relatively prime, and y is not divisible by the square of any prime.

Determine x, y and z

Good scales have equal arms (arms are the the things that connect the actual scale to the center), but in one grocery stall, the arms of the scale are not equal. Pending replacement, the manager wonders if he can give correct weight this way:

"I'll balance a 1-pound weight on the left with sugar on the right, and then I'll balance the 1-pound weight on the right with some more sugar on the left, and the sugar will add up to exactly 2 pounds."

Will it? What are other (assuming that the above works, it may not) ways of weighing 2 pounds of sugar, if you also have a lead shot with you to help weigh? (Note and hint: The lead shot has an unknown weight. You can make it whatever weight you choose. Remember, the arms aren't equal, and you need 2 pounds of sugar.)