The Perimeter is 16 + 16√2, please check it at your end.Ashetty wrote:The Perimeter of certain Isosceles right triangle is 16*16√2 . What is the length of hypotenuse of triangle??
Ans:16. How??
Thanks!!
Let us assume that hypotenuse = H and the length of 2 equal sides = S
Then H = S√2
Perimeter of the isosceles triangle = 2S + S√2 = 16 + 16√2
S(2 + √2)= 16 + 16√2
S = (16 + 16√2) / (2 + √2)
Rationalize the denominator by multiplying by its conjugate, (2 - √2):
(2 + √2)(2 - √2) = 4 - 2 = 2
Therefore, S = (16 + 16√2)(2 - √2) / 2 = (32 - 16√2 + 32√2 - 32) / 2 = 16√2 / 2 = 8√2
So, hypotenuse = 8√2 * √2 = 8 * 2 = 16
