Question

if length of hypotenuse of an isosceles right angle triangle is 10 root 2 cm then find its perimeter​

Answer 1

Step-by-step explanation:

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

Answer:

20 + 10√2

Step-by-step explanation:

Given :- Length of hypotenuse of a isosceles right angled triangle is 10√2cm

Let its equal sides be x.

According to Pythagoras Theorem

(x)2 + (x)2 = (10√2)2

2x2 = 200

x2 = 100

x = 10

So, Perimeter is x + x + 10√2

So 10 + 10 + 10√2

= 20 + 10√2