Question

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

Answer 1

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.

$ST=TU$

$4n-18=32-6n$

$4n+6n=32+18$

$10n=50$

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.

Answer 2

Answer:

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

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.

$ST=TU$

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.