Question

If the perimeter of a right angled isoceles triangle is
√2 + 1, then what is the length of the hypotenuse?

ANSWER THAT IS BEST IS BRAINLIEST

Answer 1

Let the equal sides of the isoceles right triangle be x.
Thus the length of hypoetenuse by Pythagoras theorem
Hypo^2 = (x)^2 + (x)^2
Hypo = root of 2x^
Hypo = root 2 x.
Now,
Perimeter of the triangle = root 2 + 1.
x + x + root 2 x = root 2 + 1.
x ( root 2 + 1 + 1) = root 2 + 1
x ( 2 + root 2) = root 2 + 1.
x = root 2 + 1 / 2 + root 2
After rationalizing
x = 1 / root 2
Thus,
Hypotenuse = root 2 * x
= root 2 * 1 / root
= 1
Hypoetenuse of the given isoceles right angled triangle is 1 unit.

Hope this helps you..