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

Question

 this is quadratic word problems

 

Answer 1

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.

 

 

 

Answer 2

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 :)

Answer 3

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

Answer 4

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