[urgent for tomorrow] 1. the emblem on a college banner consists of the face of a tiger inside a triangle. the lengths of the sides of the triangle are 13 cm, 14 cm, and 15 cm. is the triangle a right triangle? explain. 2. kerry has a large triangular piece of fabric that she wants to attach to the ceiling of her bedroom. the sides of the piece of fabric measure 4.8 ft, 6.4 ft, and 8 ft. is the fabric in the shape of a right triangle? explain. 3. {history} in ancient egypt, surveyors made right angles by stretching a rope with evenly spaced knots as shown. explain why the rope forms a right angle. make sure to number your answer so i know which one it is. : )

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:





We can conclude that the triangle IS a right triangle.

3. They used a  rope with 12 evenly spaced knots to represent a measure of 12 units, then, they used a section of the rope of 3 knots to represent one of the legs of a triangle and another section of 4 knots to represent the other one. Then they used the rest of the rope (5 knots) to join the two legs of the triangle. Therefore, they formed a triangle with 5 knots as its longest side and 4 and 3 knots as its shorter sides.
Lets cheek if that triangle satisfies the Pythagorean theorem:





We can conclude that their triangle es indeed a right triangle.

Where are the following equations?