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

8 units

First, find the area of the 4 by 16 rectangle. 4 times 16 is 64, so that is the area.

The area of a square is calculated with A = S^2, where A is the area and S is the side length.

So, set 64 to be the area and solve for S. 64 = S^2

The opposite of squaring something is finding the square root. So, find the square root of both sides.

square root of 64 = S

Now, what is the square root of 64? Well, what number when multiplied by itself equals 64? There are actually two possibilities here: -8 and 8. However, -8 cannot be the answer since distance cannot be negative, so 8 is the length of the side.

step-by-step explanation: