The perimeter of the quadrilateral is 41 centimeters. Find the length of each side?

Since perimeter is simply the length of the boundary of a shape, all you need to do is add up all the sides.
Doing this, we get:
x + 7 + x + 2 + x^2 - 3x + 3x - 3 = 41
x^2 + 2x + 6 = 41
x^2 + 2x - 35 = 0
Factorising,
(x + 7) (x - 5) = 0
x = -7 or 5
But x must be >0, because we cannot have negative or zero lengths.
Therefore, x = 5
Therefore, side one = 5 + 7 = 12 cm
side 2 = 7 cm
side 3 = 10 cm
side 4 = 12 cm
Hope this helps! :)

The perimeter of the quadrilateral is the sum of the lengths of all sides
Hence perimeter =x+7+x+2+x² −3x+3x−3=x²+2x+6
Hence x²+2x+6=41
or x²+2x−35=0
or x²+7x−5x−35=0
x(x+7)−(5(x+7)
(x+7)(x−5)=0
Either (x+7)= 0 i.e. x=−7 or (x−5)=0 i.e. x= 5
Taking positive values x= 5 cm
Hence the length of the sides are
First side =x+7 =5+7=12 cm
Second side =x+2=5+2=7 cm
Third side =x² −3x =5² −3×5=10 cm
Fourth side =3x−3=3×5−3=12 cm

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