The Pythagorean theorem (Chapter 7) states that, for a right triangle with sides a and b and hypotenuse c,

a. Illustrate the Pythagorean theorem for a right triangle with sides 5, 12, and 13 .

b. On the other hand, if you draw a triangle with sides measuring 2,3, and 4 units, you would find that \(2^{2}+3^{2}=4+9=13\) and \(4^{2}=16\) so \(2^{2}+3^{2} eq 4^{2}\). Also notice that such triangles are not right triangles. Is it possible to form a right triangle with sides of 25,312 , and 313 ?

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a + b = c In this chapter, we saw that a is the area of a square of side length a. We can, therefore, illustrate the Pythagorean theorem for a triangle with sides 3, 4, and 5, as shown in Figure 8.34.