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

the choices are 10 12 6 8   
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2 Answers

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
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.