Question

PS¯¯¯¯¯lies on the perpendicular bisector of QR. Select all the statements about the figure that MUST be true. Triangle P Q R with segment P S drawn from vertex P perpendicular to side Q R. S divides side Q R into two segments with lengths Q S equals 6 n plus 3 and R S equals 4 n plus 11. Sides P Q and P R are marked as congruent. A. n = 7 B. QS = 21 C. SR = 27 D. QR = 54 E. PR = 15 F. QP = 13

Answer 1

The given statements that must be true concerning the given figure are option C ( SR=27) and D (QR = 54) are true.

What is perpendicular bisector?

The perpendicular bisectors of a triangle are lines passing through the midpoint of each side which are perpendicular to the given side.

Given is a triangle as shown in the image.

Since PS is the perpendicular bisector of QR, we can write -

QS = SR

6n + 3 = 4n + 11

2n = 8

n = 4

QR = QS + SR

QR = 6n + 3 + 4n + 11

QR = 10n + 14

QR = 10 x 4 + 14

QR = 54

and

SR = 4n + 11

SR = 16 + 11

SR = 27

Therefore, of the given statements, only the option number {5} and {6} are true

Complete question:

PS lies on the perpendicular bisector of QR. Select all the statements about the figure that must be true.

A. n = 7 B. QS = 21 C. SR = 27 D. QR = 54 E. PR = 15 F. QP = 13