SOLUTION: The diagonals of a kite are (2x + 3) units and (x + 4) units. If the area is 58.5 sq. units, how long are the diagonals?

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Question 1172786: The diagonals of a kite are (2x + 3) units and (x + 4) units. If the area is
58.5 sq. units, how long are the diagonals?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonals of a kite are (2x + 3) units and (x + 4) units.
If the area is 58.5 sq. units, how long are the diagonals?
:
Area of a kite = 1%2F2a * b, where a and b are the diagonals
:
1%2F2 (2x+3)(x+4) = 58.5
multiply both sides by 2
(2x+3)(x+4) = 117
FOIL
2x^2 + 8x + 3x + 12 = 117
2x^2 + 11x + 12 - 117 = 0
A quadratic equation
2x^2 + 11x - 105 = 0
Factors to
(2x+21)(x-5) = 0
the positive solution is all we want here
x = 5
diagonal a: 2(5) + 3 = 13
diagonal b: 5 + 4 = 9
:
Check:
1%2F2*13*9 = 58.5