It might have been helpful to you to have drawn this triangle first, and then labeled the sides. I will have to assume that the length of the hypotenuse is c = 7, so that a^2 + b^2 = c^2 = 7^2 = 49.
if b = 6a, then this equation becomes a^2 + (6a)^2 = 49.
Simplifying, a^2 + 36a^2 = 49
37a^2 = 49
a^2 = 49/37
a = plus or minus 7 / sqrt(37), or plus or minus 7sqrt(37)/37.
Then b = 6a = 6(7)sqrt(37)/37. Simplify this to obtain the answer.
