Question

Which of these choices is the length of the leg of a 45-45-90 triangle with a hypotenuse of 20?

Select one:
a. 10
b. 20
c. 102√102
d. 202√

Answer 1

the answer would be b.20

Answer 2

Answer:  The correct choice is 10√2 units.

Step-by-step explanation:  We are given to select the correct choice that gives the length of the leg of a 45-45-90 triangle with a hypotenuse of 20.

Since the given triangle is an isosceles right-angled triangle, so let x units be the length of each of the legs.

Using the Pythagoras theorem, we get

$x^2+x^2=20^2\\\\\Rightarrow 2x^2=400\\\\\Rightarrow x^2=\dfrac{400}{2}\\\\\Rightarrow x^2=200\\\\\Rightarrow x=\pm\sqrt{2\times100}\\\\\Rightarrow x=\pm10\sqrt2.$

Since x is the length of the leg of the given triangle, so we get

x = 10√2 units.

Thus, the correct choice is 10√2 units.