The area of a square is represented by x2-30x+225. What is the perimeter of the square?

The sides are  x-15

 

So the perimeter is  4x-60 units

{nl} \({x}^{2}-30x+225\) right?

 

your square, by defenition, has equal length sides;

area = the length of one side squared

perimiter = the length of one side times 4

 

therefore the conversion from area to perimiter is;

     square root and times by 4

 

try quadratic factorising;

first we need some information;

     - the signs are negative and positive and therefore both signs must be negative in the brackets

     - \(\sqrt{225}=15\)

     - the question has given you the area in a 'quadraticy' way - it is likley therefore that factorising it will work

 

then do it!

 

\((x-15)(x-15)\)

 

as;

 

\(side length\times sidelength = (x-15)(x-15)\)

 

we can conclude that the length of one side is \(x-15\).

 

Next we need to find the perimiter - which is the sidelength times 4

\((x-15)\times4\)

\(4x - 60\) = perimiter

 

hope this helps