Question

Find the counterexample to one of the following statements

1). A triangle cannot have an angle that is greater than 90º .

2). The product of two positive numbers is always greater than their sum.

Answer 1

1) You know that the addition of all interior angles of a triangle always should add up to 180°

Then, for example, we can construct a triangle with angles

100°, 40°, 40° such that

100° + 40° + 40° = 180°

So we have an example of a triangle that has one angle greater than 90°.

2) Suppose that we have the positive numbers 0.5 and 1.

The product is: P = 0.5*1 = 0.5

the sum is: S = 0.5 + 1 = 1.5

The sum is greater than the product.