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

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Question 801765: The diagonals of a rhombus differ by 4. If its perimeter is 40, find its area.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
10= length of one side of the rhombus (because the perimeter, 40, is the sum of 4 such side lengths)
2x= length of the shortest diagonal
2x%2B4=2%28x%2B2%29= length of the longer diagonal (because it is 4 more than 2x)
The diagonals dplit the rhombus into 4 congruent triangles.
Applying the Pythagorean theorem to one of those 4 triangles, we get
x%5E2%2B%28x%2B2%29%5E2=10%5E2
x%5E2%2Bx%5E2%2B4x%2B4=100
2x%5E2%2B4x%2B4=100
2x%5E2%2B4x-96=0
Dividing both sides of the equal sign by 2, the equation simplifies to
x%5E2%2B2x-48=0
Solving by factoring is easy.
Factoring we get
%28x%2B8%29%28x-6%29=0 with solutions x=-8 and x=6
Since a negative length does not make sense the solution is
x=6, which makes x%2B2=8
The area of the rhombus is the area of the 4 triangles
2%2A6%2A8=highlight%2896%29