SOLUTION: The diagnol of the rectangle is 15 cm. Permimeter is 38cm. What is the area? Is it possible to find the answer without finding out the dimensions of the rectangle?

Algebra ->  Rectangles -> SOLUTION: The diagnol of the rectangle is 15 cm. Permimeter is 38cm. What is the area? Is it possible to find the answer without finding out the dimensions of the rectangle?      Log On


   

Question 146784: The diagnol of the rectangle is 15 cm. Permimeter is 38cm. What is the area?
Is it possible to find the answer without finding out the dimensions of the rectangle?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
P=2%28L%2BW%29 Start with the perimeter formula


38=2%28L%2BW%29 Plug in P=38


19=L%2BW Divide both sides by 2. So L%2BW=19


L%5E2%2BW%5E2=D%5E2 Now move onto the Pythagorean equation dealing with the diagonal and the side lengths


L%5E2%2BW%5E2=15%5E2 Plug in D=15


L%5E2%2BW%5E2=225 Square 15 to get 225


L%5E2%2BW%5E2%2B2LW-2LW=225 Now add and subtract the quantity 2LW on the left side. Adding and subtracting the same quantity does not change the equation.


%28L%5E2%2B2LW%2BW%5E2%29-2LW=225 Group the terms


%28L%2BW%29%5E2-2LW=225 Factor L%5E2%2B2LW%2BW%5E2 to get %28L%2BW%29%5E2


%2819%29%5E2-2LW=225 Plug in L%2BW=19


361-2LW=225 Square 19 to get 361


361-2A=225 Now replace LW with A. Remember, A=LW


-2A=225-361 Subtract 361 from both sides.


-2A=-136 Combine like terms on the right side.


A=%28-136%29%2F%28-2%29 Divide both sides by -2 to isolate A.


A=68 Reduce.


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Answer:

So the answer is A=68


So given a diagonal of 15 cm and a perimeter of 38 cm, the area is 68 cm%5E2



Note: You can go another way and solve for L and W (which turn out to be %2819-sqrt%2889%29%29%2F2 and %2819%2Bsqrt%2889%29%29%2F2) and find the area by multiplying L and W