The perimeter of an isosceles right triangle is 16 + 16√2. Whats the length of the hypotenuse?

By definition, an isosceles right triangle has two legs of the same length. If we let x denote the first leg and x denote the second, we get:

x^2 + x^2 = c^2 (the hypotenuse)

==> c^2 = 2x^2

==> c = x√2

Since the perimeter is 16 + 16√2:

x + x + x√2 = 16 + 16√2

==> (2 + √2)x = 16 + 16√2

==> x = (16 + 16√2)/(2 + √2)

==> x = 8√2

Therefore, the length of the hypotenuse is x√2 = (8√2)(√2) = 16 (Answer B).

I hope this helps!

If hypotenuse length is h then legs are (h√2)/2 Perimeter is h +h√2 = h(1+√2) For what is necessary DE the mid segment

Definition Of Isosceles Right Triangle

Let the hypotenuse be represnted as h and the equal sides as s

2s + h (that is the perimeter) = 16 + 16√2.

2s^2 = h^2

h^2/s^2 = 2

h/s = √2

h = s√2

2s + s√2 = 16 + 16√2

s(2 + √2) = 16 + 16√2

s = (16 + 16√2)/(2 + 2√2)

h = s√2 = √2 (16 + 16√2)/(2 + 2√2)

h = (16√2 + 16)/(2 + 2√2)

h = 16(√2 + 1)/2(1 + √2)

h = 8(1 + √2)/(1 + √2) = 8

Correct answer option:

a. 8

An isosceles right triangle is a 45-45-90 Triangle.

There are several ratios involved when dealing with these

Side opposite the 45 is a

and the hypotenuse is a sqrt 2

Thus if the legs are 8 then the hypotenuse is 8 sqrt 2

If the legs are 8 sqrt 2 then the hypotenuse is (8 sqrt 2) (sqrt 2) = 16; which is the answer in this case

B.16

I dont know the answer but the formula is A^2+B^2=C^2