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

Question 801765: The diagonals of a rhombus differ by 4. If its perimeter is 40, find its area.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= length of one side of the rhombus (because the perimeter, 40, is the sum of 4 such side lengths)
= length of the shortest diagonal
= length of the longer diagonal (because it is 4 more than )
The diagonals dplit the rhombus into 4 congruent triangles.
Applying the Pythagorean theorem to one of those 4 triangles, we get

Dividing both sides of the equal sign by 2, the equation simplifies to

Solving by factoring is easy.
Factoring we get
with solutions and
Since a negative length does not make sense the solution is
, which makes
The area of the rhombus is the area of the 4 triangles

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