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# the area of a square is 165 cm greater than its perimeter. what is the length of the side of this square?

### 4 Answers by Expert Tutors

Artem N. | Experienced school-level and beyond math and computer tutorExperienced school-level and beyond math...
5.0 5.0 (179 lesson ratings) (179)
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side - x
area - x2
perimeter - 4x
x2 - 4x = 165
x2 - 4x - 165 = 0
D = (-4)2 + 165*4 = 676
x1 = (4 + 26) / 2 = 15
x2 = (4 - 26) / 2 = -11

Disregard x2 since it is negative

Answer is : side of the square is 15cm.

4.9 4.9 (233 lesson ratings) (233)
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Hey Raven -- an intuitive approach ... perimeter 4d must be an even # ...

area d*d seems to be an odd multiple of 5 to produce an "offset" of 165 ... 5x5 too small

... try 15x15 ==> 225 minus 60 is 165 ==> d= 15cm ... Best regards :)
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi Raven;
perimeter=4x
area=x2
x2=4x+165
x2-4x-165=0
For the FOIL...
FIRST must be (x)(x)=x2
OUTER and INNER must add-up to -4x.
LAST must be (11)(15) or (15)(11) and one number must be negative to render the product of -165.
(x+11)(x-15)=0
Let's FOIL...
FIRST...(x)(x)=x2
OUTER...(x)(-15)=-15x
INNER...(11)(x)=11x
LAST...(11)(-15)=-165
x2-15x+11x-165=0
x2-4x-165=0
(x+11)(x-15)=0
Either parenthetical equation must equal zero...
x+11=0
x=-11--not applicable.  Measurements cannot be negative.
x-15=0
x=15
Let's check our work...
x2=4x+165
(15)2=[(4)(15)]+165
225=60+165
225=225
Tom D. | Very patient Math Expert who likes to teachVery patient Math Expert who likes to te...
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I don't like the way this question is phrased because it is mixing an area (cm^2) with the linear dimension of perimeter (cm).  That is never good practice.  We'll assume the question addresses the magnitude of the area (cm^2) with the perimeter (cm).

s^2 = 4s + 165
s^2 - 4s - 165 =0

(S+11)(S-15) =0  --->S=15 cm