Question

In ΔPQR point s is midpoint of side QR if PQ = 11 , PR = 17 , PS = 13 then find the length of QR. ​

Answer 1

Answer:

QR:6

Step-by-step explanation:

PR:PS+SR

17:13+SR

17-13:SR

4:SR

PQ:PS+QS

11:13+QS

11-13:QS

2:QS

QR:QS+SR

QR:2+4

QR:6

Answer 2

Given :-

• Point S is midpoint of side QR.
• PQ = 11 , PR = 17 , PS = 13

To Find :-

• Length of QR.

Solution :-

↪In ΔPQR, Seg PS is median. (According to Definition)

According to Appollonius theorem,

⭐ PQ² + PR² = 2PS² + 2QS²

[ Putting values ]

↪ 11² + 17² = 2(13)² + 2QS²

↪ 121 + 289 = 2(169) + 2QS²

↪ 410 = 338 + 2QS²

↪ 410 - 338 = 2QS²

↪ 72 = 2QS²

↪ QS² = 36

↪ QS = 6

Now,

Given, point S is midpoint of side QR.

⭐ QS = 1/2 × QR

[ Putting values ]

↪ 6 = 1/2 × QR

↪ 6 × 2 = QR

↪ QR = 6 × 2

↪ QR = 12

Hence,

• The length of QR is 12 unit.