Respuesta :

Answer:

The value of n is 5 and the length of side SU is 4 units.

Step-by-step explanation:

It is given that RT is the perpendicular bisector of SU.

It means RT bisects the line SU and T is the midpoint of SU.

Since T is the midpoint of SU, therefore the distance of T from S and U are same.

[tex]ST=TU[/tex]

[tex]4n-18=32-6n[/tex]

[tex]4n+6n=32+18[/tex]

[tex]10n=50[/tex]

Divide both sides by 10.

[tex]n=5[/tex]

The value of n is 5.

[tex]SU=ST+TU[/tex]

[tex]SU=4n-18+32-6n[/tex]

[tex]SU=-2n+14[/tex]

Put n=5,

[tex]SU=-2(5)+14[/tex]

[tex]SU=4[/tex]

The length of side SU is 4 units.

Answer:

[tex]n=5\text{ and }SU=4\text{ units}[/tex]

Step-by-step explanation:

Given information: RT is the perpendicular bisector of SU, ST=4n-18 and TU=32-6n.

It is given that RT is the perpendicular bisector of SU. It means RT divides SU in two equal parts at T.

[tex]ST=TU[/tex]

Substitute the given values.

[tex]4n-18=32-6n[/tex]

[tex]4n+6n=32+18[/tex]

[tex]10n=50[/tex]

Divided both sides by 10.

[tex]n=5[/tex]

The value of n is 5.

[tex]ST=TU=32-6(n)=32-6(5)=32-30=2[/tex]

We need to find the measure of SU.

[tex]SU=ST+TU[/tex]

[tex]SU=2+2[/tex]

[tex]SU=4[/tex]

Hence, the measure of SU is 4 units.

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