In an isosceles right triangle, the ratio of the length of the hypotenuse to the length of a leg is...

Question

a) √3 : 1

b) √2 : 1

c) 1 : 1

d) 2 : 1

Please help ):

Answer 1

Let x = length of a leg

 

By the Pythagorean Theorem, (hypotenuse)² = x²+x²

 

                                            (hypotenuse)² = 2x²

 

                                             hypotenuse = √2x

 

So, hypotenuse / leg = (√2x) / x = √2 / 1