Answered

If TU = 6 units, what must be true?


SU + UT = RT


RT + TU = RS


RS + SU = RU


TU + US = RS

If TU = 6 units, what must be true? SU + UT = RT RT + TU = RS RS + SU = RU TU + US = RS class=

Verified Answer :

carlosego

From the figure we can see that:

\(RS = 24

RT = 12
\)

In addition, we have to:

\(TU = 6
\)

Therefore, the value of SU is given by:

\(SU = RS - (RT + TU)
\)

Substituting values we have:

\(SU = 24 - (12 + 6)

SU = 6
\)

Therefore, it is true that:


\(SU + UT = RT
\)

Verifying we have:

\(6 + 6 = 12
\)

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

\(SU + UT = RT\\6 + 6 = 12\)

Thus, the statement is true.

B.) RT + TU = RS

substitute values

\(RT + TU eq RS\\12 + 6 eq 24\)

Thus, the statement is not true.

C.) RS + SU = RU

substitute values

\(RS + SU eq RU\\24+6 eq 18\)

Thus, the statement is not true.

D.) TU + US = RS

substitute values

\(TU + US eq RS\\6+6 eq 24\)

Thus, the statement is not true.

Hence, only statement A is true.

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