SOLUTION: the area of a square is 21 more than the perimeter. Find the length of a side

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Question 168739: the area of a square is 21 more than the perimeter. Find the length of a side
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"the area of a square is 21 more than the perimeter" ----> A=P%2B21


Remember, the area of a square is A=s%5E2 and the perimeter of a square is P=4s where "s" is the side length

So A=P%2B21 becomes s%5E2=4s%2B21


s%5E2-4s-21=0 Subtract 4s from both sides. Subtract 21 from both sides.



%28s-7%29%28s%2B3%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:


s-7=0 or s%2B3=0


s=7 or s=-3 Now solve for s in each case



Now discard the solution s=-3 since a negative side length does not make sense.


So the answer is s=7 which means that the length of the side of the square is 7 units