Question

Select all the statements about the figure that MUST be true. Р Q 6n + 3 S 4n + 11 R PR=15 QS=21 QP=13 n=7 SR=27 QR=54​

Answer 1

Options (5) and (6)

Explanation:

From the picture attached,

In right triangle ΔPSQ and ΔPSR,

PS ≅ PS [By reflexive property]

PQ ≅ PR [Given]

ΔPSQ ≅ ΔPSR [By HL property of congruence]

Therefore, QS ≅ SR [CPCTC]

(6n + 3) = (4n + 11)

6n - 4n = 11 - 3

2n = 8

n = 4

QS = (6n + 3)

= 6×4 + 3

= 27

SR = (4n + 11)

= 4×4 + 11

= 16 + 11

= 27

QR = QS + SR

= 27 + 27

= 54

Therefore, Options (5) and (6) are the correct options.