Aright triangle has side lengths 4 units, 5units, and x units. it is unknown if the missing length is the longest or shortest side. rounded to the nearest tenth, what is the difference between the possible values of x?

3rd Option is correct.

Step-by-step explanation:

Given: A right angles triangle.

          length of the sides of triangle are 4 units , 5 units and x units.

we have to find difference between possible value of x.

We use Pythagoras theorem of right angled triangle to fins the value of x.

Pythagoras theorem states that square of the hypotenuse is equal to the sum of the square of the legs of the triangle.  

If x is longest side that is hypotenuse.

then using Pythagoras theorem,  

x² = 4² + 5²

x² = 16 + 25

x² = 41

x = √41

x = 6.40 units

If x is shortest side ⇒ 5 is length of hypotenuse.

then using Pythagoras theorem,  

5² = 4² + x²

25 = 16 + x²

x² = 25 - 16

x² = 9

x = √9

x = 3 units

Difference of x = 6.40 - 3 = 3.40 unit

Therefore, 3rd Option is correct.

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.