Hi...........

Formula for area of square is Given by= x^2 where x is the length of side of square.

suppose the actual length of square is X cm.

so actual area= X^2

now as given in problem area is increased by 5 cms. so new length= X+5

thus new area= (X+5)*(X+5)

(X+5)*(X+5)=144cm^2

thus X^2 +10*X + 25=144

X^2 +10*X -119=0

It is a quadratic equation.

Now using the principle of factorization it can be solved as follows

X=  (-10 +(10*10-4*1*(-119))^1/2)/2*1 or X=(-10 -(10*10-4*1*(-119))^1/2)/2*1

using the formula of quadratic equation   for equation of type a*x^2 + b*x +c=0 (X=-b +-(b^2 +4*a*c)^1/2)/2*a

here a=1 b=10 and c=-119

thus X=(-10 +24)/2 and X=(-10-24)/2

X=14/2 and X=-34/2

X=7 and X=-17

as we now that length cannont be negative so actual length of square will be

X=7cms