Question

The sides in centimeter of a triangle are x-y,

2√xy and x+y. Show that it is a right angled triangle

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Let's assume the sides of the triangle are x-y, 2√xy, and x+y.

Now, let's calculate the squares of these sides:
(x-y)^2 = x^2 - 2xy + y^2
(x+y)^2 = x^2 + 2xy + y^2
(2√xy)^2 = 4xy

Now, let's check whether the Pythagorean theorem holds for this triangle:
(x-y)^2 + (2√xy)^2 = (x+y)^2
(x^2 - 2xy + y^2) + 4xy = x^2 + 2xy + y^2

Simplify the equation:
x^2 - 2xy + y^2 + 4xy = x^2 + 2xy + y^2
x^2 + 2xy + y^2 = x^2 + 2xy + y^2

Since both sides of the equation are equal, the sides x-y, 2√xy, and x+y satisfy the Pythagorean theorem. This means that the triangle is a right-angled triangle.