Question

in a right angled triangle if the square of hypotenuse is twice the product of other two sides then one of the angles of the triangle is?

Answer 1

Let the three sides of triangle are base(x), perpendicular(y) and hypotenuse(z)
then according to the given condition z^2 = 2x*y
or x^2 + y^2 = 2x*y 
or (x-y)^2 = 0
or x = y
so triangle is isosceles and angle = 45 , 45 and 90

Answer 2

Answer:

One angle of the two angles of the right angle triangle is 45°

Step-by-step explanation:

In a right angle triangle, square of hypotenuse is twice the product of other two sides.

Therefore, h² = 2xy ------(1)

From Pythagoras theorem,

x² + y² = h²------(2)

From equation (1) and equation (2),

x² + y² = 2xy

x² + y² - 2xy = 0

(x - y)² = 0

x - y = 0

x = y

Both the sides of the right angle triangle are equal.

In ΔABC angles opposite to these sides will be equal.

We know sum of all angles in a right angle triangle is 180°

Therefore, m∠A + m∠B + m∠C = 180°

m∠A + 90° + m∠C = 180°

2(m∠A) = 180 - 90 = 90° [Since ∠A ≅ ∠C]

m∠A = 45°

Therefore, one angle of the triangle is 45°.

Learn more about the properties of the triangle from https://brainly.in/question/2383861