QUESTION 1The term Pythagorean triple is intended to explain that if three different positive integers, each measuring the distance of one side of a right triangle, (usually known as a, b and side1, side2 and side3) satisfy the rule a2 + b2 = c2 so the combination of these numbers is a Pythagorean triple. The concept is correct only when the triangle used is a right triangle because there must be a hypotenuse opposite the right angle. The proof used consists of three triangles, each of which uses positive integers, they are right triangles and they all respect the rule a2 + b2 = c2, which means they are Pythagorean triples. Rule〖side〗_1^2+〖side〗_2^ 2=〖hyp〗^2〖 a〗^2+b^2=c^2 or c = √(a^2+b^2 ) Triangle 1 a = scale 3 cm b = 4 cm 1 cm = 1 cm c = 5 cm ∴1 :1〖 a〗^2+b^2=c^2〖 3〗^2+4^2=5^29+16=25 〖 c〗^2=25 c=√25 c=5Triangle 2 a = 8 cm scale b = 15 cm 1 cm = 1 cm c = 17 cm ∴1:1〖 a〗^2+b^2=c^2 〖 8〗^2+〖15〗^2=〖17〗^264+225=289〖 c 〗^2=289 c=√289 c=17triangle 3 a = scale 6 cm b = 8 cm 1 cm = 1 cm c = 10 cm ∴1:1〖 a〗^2+b^2=c^2〖 6〗^2+8 ^2=〖10〗^236+64=100〖 c〗^2=100 c=√ 100 c=10QUESTION 2The Pythagorean theorem proves that a2 + b2 = c2 but his theorem is applicable only to right triangles. Although isosceles can be right triangles because two sides are the same length, the formula doesn't work. In most cases; if a^2+b^2=c^2 then the triangle is right angled if a^2+b^2 is large...... half the paper...... be able to prove the law with the cube the formula would be a3 + b3 = c3 but this formula doesn't work when used in a real problem. This premise is flawed because it attempts to translate a theorem applicable in two dimensions (squares) into three dimensions (cubes). If this premise were possible it would imply a fixed ratio between area and volume. For example〖a 〗^3+b^3=c^3〖 3〗^3+4^3=5^327+64=125Which is incorrect because 27 + 64 is actually equal to 91If the 3D premise were able to prove the Pythagorean theorem, the premise should be refined. Therefore, a possible way to refine the premise is to adapt to the choice of 3D shape used. The 3D shape chosen to replace the cube is a pyramid with a triangular base. This premise is also flawed as it does not fit the Pythagorean law. Therefore it is proven that 3D shapes are not applicable to Pythagoras' law.