What is the relationship between the side and diagonal of a square?

READ the instructions on the right and INTERACT with the GeoGebra applet below.

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Investigation Steps

Click on the reset icon icon to reset the diagram.

 Step 1 Close 

Move points A or B to change the size of the square. Note the measures of square (side and its diagonal) and record them. Sort the data by the length of S, and create a table with 4 colunms.


 Step 2 Close 

Number Side Diagonal Ratio (D/S)
1

Find the ratio of the length of the diagonal to the length of the side of each square, rounded to two digits after the decimal point.


 Observations and Remarks Close 

Squares with longer sides (S) have longer diagonals (D).

The ratios D/S are almost equal. Or even better, D/S = C, where C is the √2, which is approximately equal to 1.4148.

In algebra the same thing can be written in many different ways. If D/S = C, then D = C × S. Therefore we may also write our conclusion as D = C × S.