+128475 Let S = (0,0)
M = (0,2)
P = (2,2)
The area of the trapezoid = (1/2)MS (MP + SR) = (1/2) (2) ( 2 + 3) = 5
So....1/2 the area of the trapezoid = 5/2
Which means that
(5/2) =(1/2) MS ( MP + SQ)
5 = MS (MP + SQ)
5 = (2) ( 2 + SQ)
5 = 4 + 2SQ
5 - 4 = 2SQ
1 = 2SQ
SQ = 1/2 so Q = ( 1/2 , 0)
So PQ = sqrt [ ( 2 - 1/2)^2 + 2^2 ] = sqrt [ (1.5)^2 + 4] = sqrt [ 2.25 + 4 ] = sqrt 6.25 = 2.5 =
2 5/10 = 25 /10 = 5/2 = n/m
So
m + n = 2 + 5 = 7
