A right triangle has the side legnths 4 units, 5 units, 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 ?

For longest x = 6.4

For shortest x = 3

Step-by-step explanation:

Given a right angle triangle with lengths 4 units and 5 units and x units .

x can be gotten using Pythagoras theorem .

If x Is the longest side , then

x^2 = 5^2 + 4^2

= 5x5 + 4x4

= 25 + 16

x^2 = 41

x = squared root of 41

x = 6.4

If x is the shortest side ,

x^2 = 5^2 - 4^2

= 5x5 - 4x4

= 25 - 16

x^2 = 9

x = squared root of 9

x = 3

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.