Question 168667: The perimeter and the diagonal of a rectangle are 18m and 5 m respectively. find its area ?
Found 2 solutions by stanbon, jojo14344:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The perimeter and the diagonal of a rectangle are 18 and 5 m respectively. find its area ?
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perimeter = 18m
diagonal = 5m ?
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Perimeter = 2(L+W) = 18m
L+W = 9m
L = 9m-W
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Using Pytagoras:
w^2 + (9m-W)^2 = (5m)^2
W^2 + 81m^2 - 18mW + w^2 = 25m^2
56m^2 -18wm +2w^2 = 0
28m^2 - 9wm + 2w^2 = 0
m = [9w +- sqrt(81w^2 -4*28*2w^2)]/56
m = [9w +- sqrt(-143w^2)]/56
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Comment: Since you have a negative radicand you have no Real Number solution.
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Cheers,
Stan H.
Cheers,
Stan H.
Answer by jojo14344(1513) (Show Source):
You can put this solution on YOUR website! That forms 2 Right Triangles with the diagonal right?
See below,
In a Pyth. theorem, a Right Triangle with  (diagonal), has other sides measure:  and 
Proof: Pyth.Theorem:
 , good
.
Therefore, 
Since it forms 2 triangles:
*Note: 
.
 , ANSWER
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*Now, this is misleading data, having  . It doesn't make sense. If we calculate  , Does not match up. PLEASE VERIFY THIS.
Thank you,
Jojo
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