Respuesta :

carlosego

From the figure we can see that:

[tex] RS = 24

RT = 12
[/tex]

In addition, we have to:

[tex] TU = 6
[/tex]

Therefore, the value of SU is given by:

[tex] SU = RS - (RT + TU)
[/tex]

Substituting values we have:

[tex] SU = 24 - (12 + 6)

SU = 6
[/tex]

Therefore, it is true that:

[tex] SU + UT = RT
[/tex]

Verifying we have:

[tex] 6 + 6 = 12
[/tex]

Answer:

The following must be true:

SU + UT = RT

Only statement A is true. And the length of the US is 6 units.

Given to us

  • RS = 24 units
  • RT = 12 units
  • TU = 6 units

What is the Length of SU?

Length of SU = RS - RT - TU

                      = 24 - 12 - 6

                      = 24 - 18

                      = 6

Thus, the length of the US is 6 units.

Now let's check all that are true,

A.) SU + UT = RT

substitute values

[tex]SU + UT = RT\\6 + 6 = 12[/tex]

Thus, the statement is true.

B.) RT + TU = RS

substitute values

[tex]RT + TU \neq RS\\12 + 6 \neq 24[/tex]

Thus, the statement is not true.

C.) RS + SU = RU

substitute values

[tex]RS + SU \neq RU\\24+6\neq 18[/tex]

Thus, the statement is not true.

D.) TU + US = RS

substitute values

[tex]TU + US \neq RS\\6+6\neq 24[/tex]

Thus, the statement is not true.

Hence, only statement A is true.

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