Question

1.Two right triangles are drawn below find the lengths of all the sides for both ABC and AED2.What do you notice about the relationship between the side length of ABC compared to the side lengths of AED3.justify why this relationship exist and explain how you can use this relationship to find other Pythagorean triples

Answer 1

Let the length of each square box on the graph be 1 unit

In △ABC

AB = 3 units

AC = 4 units

BC = √ (3² + 4²) (Using the Pythagoras theorem)

BC = √25

BC = 5

In △AED

AE = 6 units

AD = 8 units

ED = √ (6² + 8²) (Using the Pythagoras theorem)

ED = √(36+64)

ED = √100

ED = 10

The side lengths of △AED are twice the sidelengths of △ABC because they are similar triangles with a scale factor of 2

A pythagoran triple that will also obey the relationship a² = b² + c² can also be formed using the scale factor to find the lengths of the new sides.