Question

if the perimeter of right angled isosceles triangle is root 2 + 1 units then find the length of the hypotenuse

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..

Answer 2

Let the Base be a
Perpendicular = a

Hypotenuse = root (a^2 +a^2)
= a *root 2

According to question
Perimeter = (root 2) + 1
=> a+a+a root 2 = (root2) + 1
=> a (1+1+root2) = root2 + 1
=> a(2 +root2) = 1+ root2
=> a = (1+root2) / (2+ root2) -------(1)

Hypotenuse = a *root 2
= (1+root2) (root2) / (2+root2)
= (root2 + 2)/ (2+root2)
= 1


Hypotenuse = 1 Unit


Hope it will help you

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