If a 4 × 16 rectangle has the same area as a square, what is the length of a side of the square?

Question

the choices are 10 12 6 8   

Answer 1

Find the area of the rectangle first.

 

Area = 4 x 16 = 64 square units

 

 

Then take the square-root of this value to find the side length of square.

 

length of square = √64 = 8 units

 

 

 

 

Or you can set up an equation to reduce the number of steps.

 

Area of rectangle = Area of square

 

(4 x 16) = x²

 

where x is the length of square.  From here, solve for x.

 

64 = x²

 

8 = x

Answer 2

8 is the answer.  The area of a square with sides of 8 is 8x8 or 64 units, the same as a rectangle with 2 sides of 4 and 2 sides of 16 units.