SOLUTION: The perimeter and the diagonal of a rectangle are 18m and 5 m respectively. find its area ?

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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(48545) About Me  (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.
=====================================
Cheers,
Stan H.




Cheers,
Stan H.

Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!
That forms 2 Right Triangles with the diagonal right?
See below,
drawing%28200%2C200%2C-1%2C50%2C-1%2C30%2Cred%28line%281%2C1%2C50%2C1%29%29%2Cline%2850%2C1%2C50%2C20%29%2Cline%2850%2C20%2C1%2C20%29%2Cred%28line%281%2C20%2C1%2C1%29%29%2Cred%28line%281%2C20%2C50%2C1%29%29%2Clocate%2818%2C16%2C5m%29%2Clocate%2825%2C25%2CP=18m%29%29
In a Pyth. theorem, a Right Triangle with hypotenus=5m (diagonal), has other sides measure: opposite=Width=3m and adjacent=Length=4m
Proof: Pyth.Theorem:
5%5E2=3%5E2%2B4%5E2
25=9%2B16
25=25, good
.
Therefore, Area=%281%2F2%29bh=%281%2F2%29L%2AW=%281%2F2%293%2A4
Area=6m%5E2=A%5B1%5D=A%5B2%5D
Since it forms 2 triangles:
Area%5BR%5D=A%5B1%5D%2BA%5B2%5D
*Note: A%5B1%5D=A%5B2%5D
drawing%28200%2C200%2C-4%2C50%2C-3%2C30%2Cred%28line%281%2C1%2C50%2C1%29%29%2Cline%2850%2C1%2C50%2C20%29%2Cline%2850%2C20%2C1%2C20%29%2Cred%28line%281%2C20%2C1%2C1%29%29%2Cred%28line%281%2C20%2C50%2C1%29%29%2Clocate%2818%2C16%2C5m%29%2Clocate%2812%2C8%2CA%5B1%5D%29%2Clocate%2837%2C13%2CA%5B2%5D%29%2Clocate%28-4%2C10%2C3m%29%2Clocate%2812%2C-1%2C4m%29%29%29
.
Area%5BR%5D=6m%5E2%2B6m%5E2=highlight%2812m%5E2=A%5BR%5D%29, ANSWER
.
*Now, this is misleading data, having P=18m. It doesn't make sense. If we calculate Perimeter=2%28L%2BW%29=2%283%2B4%29=2%287%29=14m , Does not match up. PLEASE VERIFY THIS.
Thank you,
Jojo