The mathematics of the early Egyptians was practical and centered around surveying, construction, and recordkeeping. They used a simple device to aid surveying - a rope with 12 equal divisions marked by knots, as shown in Figure 7.56. When the rope was stretched and staked so that a triangle was formed with sides 3,4 , and 5 , the angle formed by the shorter sides was a right angle. This method was extremely useful in Egypt, where the Nile flooded the rich lands close to the river each year. The lands needed to be resurveyed when the waters subsided. Which of the following ropes would form right triangles?

Rope $A$ : 30 knots (sides 5, 12, and 13)

Rope $B$ : 9 knots (sides 2, 3, and 4) 

Figure 7.56

Transcribed Image Text:

5 5 4 3