1. The emblem on a college banner consists of the face of a tiger inside a right triangle. The lengths of two sides of the triangle are
13 centimeters and 14 cm.
What is the length of the longest side of the right triangle?

1. For a triangle to be a right triangle, it must satisfy the Pythagorean theorem: ; the square of the longest side (hypotenuse) of the triangle is equal to the sum of the squares of its shorter sides.
We know from our problem that the longest side of our triangle is 15 cm long and the shorter sides are 13 cm and 14 cm respectively, so:

We can conclude that the triangle is NOT a right triangle.

2. Just as before, for a triangle to be a right triangle, it must satisfy the Pythagorean theorem: ; the square of the longest side (hypotenuse) of the triangle is equal to the sum of the squares of its shorter sides.
We know from our triangle that its longest side is 8 ft long and its shorter sides are 4,8 ft and 6.4 ft, so lets use the Pythagorean theorem: