Question 78327
Since the areas are equal we can find the area of the rectangle to find the area of the square:


Area of rectangle=base*height=24*30=720

So the area of the rectangle is 720 square centimeters. Now we know the area of the square is 720 square centimeters also. Now we have this relationship:

Area of square=side*side=(side)^2


Let s=side

So we have

Area of square

{{{A=s^2}}}

{{{720=s^2}}} Plug in A=720 and solve for s

{{{sqrt(720)=sqrt(s^2)}}} take the square root of both sides

{{{s=sqrt(720)}}}

Now reduce:

{{{s=sqrt(144*5)}}}

{{{s=sqrt(144)*sqrt(5)}}}

{{{s=12*sqrt(5)}}}

So the side of the square is about 26.83 cm long