SOLUTION: The diagonals of a rhombus differ by 4. If the perimeter is 40, find its area.

Question 1012047: The diagonals of a rhombus differ by 4. If the perimeter is 40, find its area.
Answer by ValorousDawn(53) (Show Source): You can put this solution on YOUR website!
Lets say the shorter diagonal has length 2x, and the longer one is of length 2x+4. The center to each vertex is therefore x and x+2. Using the Pythagorean theorem, the length of each side of the diagonal is
Which equates to
There are four of these lengths, and the sum of those four is the perimeter-40. Thus, we have

The negative answer doesn't work, because negative distance doesn't exist. Our answer is therefore x=6.
The diagonals are thus 12, and 16. The area of a rhombus given by it's diagonals are so the area is

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