Question

What is the length of the longer diagonal of a rhombus if its area is 16 and the length of one of the diagonals is 8?

Answer 1

The area for a rhombus is $A= \frac{1}{2}( d_{1} d_{2} )$.  We have the area and the length of one of the diagonals, so we fill in accordingly: $16= \frac{1}{2} (8x)$.  8x/2 = 4x, so now we have 16=4x.  Divide both sides by 4 to get x = 4.  It's not longer than 8, but it's the length of the other diagonal, for sure.