A rectangular field of length (X+5) metres is (x-2) metres wide. If the diagonal is (X+6) metres. Find
(A) the value of X
( B) the area of the field
so...
(x+5)^2 + (x-2)^2 = (x+6)^2
x^2 + 10x + 25 + x^2 - 4x + 4 = x^2 + 12x + 36
x^2 - 6x -7 = 0
(x-7)(x+1) = 0
x = 7 or x = -1, but x = -1 would make one of the sides negative, so
x = 7
length = 12 m, width = 5 m
area = 60 m^2