Question

PLS HELP!!! 20 pts!!!!

1. If QR = 12 and QR is a perpendicular bisector of TS, determine which of the following claims are true.

Answer 1

see explanation

Explanation:

Since QR is a perpendicular bisector then Δ RST is isosceles

with 2 congruent legs , that is

RT = RS , substitute values

6x - 4 = 3x + 8 ( subtract 3x from both sides )

3x - 4 = 8 ( add 4 to both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Then RS = 3x + 8 = 3(4) + 8 = 12 + 8 = 20

so RT = RS = 20

Using Pythagoras' identity in right triangle QRT

QT² + QR² = RS²

QT² + 12² = 20²

QT² + 144 = 400 ( subtract 144 from both sides )

QT² = 256 ( take square root of both sides )

QT =
`√(256)` = 16

In summary

RS = 12 is False ( RS = 20 )

x = 4 is True

x = 3 is False

QT = 16 is True