Question

In a right angled triangle , one acute angle is double the other. Prove that hypotenuse is double the smallest side.

Answer 1

Let one acute be x
So, the other becomes 2x
In right angled triangle,
(hypotenuse)^2 = (base)^2 + (perpendicular)^2
(hypotenuse)^2 = x^2 + (2x)^2
(hypotenuse)^2 = x^2 + 4x^2
(hypotenuse)^2 = 5x^2
hypotenous = sqrt(5x^2)
hypotenuse = sqrt(5) *x
the inference given in the question is wrong, hypotenuse is root 5 times the smallest side