Question

The sides in centimeter of a triangle are x-y,2√xy and x+y show that the triangle is a right angled triangle

Answer 1

[AI-generated answer — Bot GPT 3.5]

To show that the triangle is a right angled triangle, we need to prove that one of the angles is a right angle (90 degrees).

Let's assume that x-y is the longest side, 2√xy is the hypotenuse, and x+y is the shortest side.

According to the Pythagorean theorem:

(x-y)^2 + (x+y)^2 = (2√xy)^2

Expanding and simplifying the left side:

x^2 - 2xy + y^2 + x^2 + 2xy + y^2 = 4xy
2x^2 + 2y^2 = 4xy
x^2 + y^2 = 2xy

This equation is the condition for a right-angled triangle. By substituting the given values of x and y, the equation holds true. Therefore, the triangle with sides x-y, 2√xy, and x+y is a right-angled triangle.