Question

Please help ! RT is the perpendicular bisector of SU. Find the value of n and SU.

Answer 1

`n=5\text{ and }SU=4\text{ units}`

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.

`ST=TU`

Substitute the given values.

`4n-18=32-6n`

`4n+6n=32+18`

`10n=50`

Divided both sides by 10.

`n=5`

The value of n is 5.

`ST=TU=32-6(n)=32-6(5)=32-30=2`

We need to find the measure of SU.

`SU=ST+TU`

`SU=2+2`

`SU=4`

Hence, the measure of SU is 4 units.

Answer 2

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

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.

`ST=TU`

`4n-18=32-6n`

`4n+6n=32+18`

`10n=50`

Divide both sides by 10.

`n=5`

The value of n is 5.

`SU=ST+TU`

`SU=4n-18+32-6n`

`SU=-2n+14`

Put n=5,

`SU=-2(5)+14`

`SU=4`

The length of side SU is 4 units.