What is the length of the hypotenuse in the right triangle shown below?

A. 6 √2

Step-by-step explanation:

If a triangle is a 45-45-90 triangle then,

Theorem 5-13: If each acute angle of a right triangle has a measure of

45 degrees, then the measure of the hypotenuse is the square root of two times as long as a  leg (45, 45, 90 Theorem).

so the hypotenuse is x√2, and x = 6 (side length)

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.