The area of a rhombus is 337.5 square millimeters. If one diagonal is three times as long as the other, what are the lengths of the diagonal

Let's look at this one, again

Call the length of the longer diagonal 3L, and the shorter diagonal, L

So

337.5  = (L)(3L) / 2

337.5 = (3/2)L^2   multiply both sides by 2/3

225 = L^2     take the square root of both sides

225 = L  = 15cm and that's the shorter diagonal

So...the longer one is 3(15)  = 45cm

337.5=d1xd2/2

lets make it easy. the formula for a rhombus is d1xd2/2

if one diagonal is 3x longer than the other, it will be 3x.

337.5=X*3x/2

multiply out the dividing 2

675=x*3x

divide by three and that is your answer for x

225=x 3x=675