Question

In ΔPQR, point S is the midpoint of side QR.If PQ=11,PR=17,PS=13, find QR.

Answer 1

Final Answer: 12 cm

Steps;

1) In right ΔPQR,

we have

PQ=11 units ,PR=17 units ,SR = ? ,PS=13 units

By Apollonus's Theorem,

$PQ^{2} + PR^{2} = 2(PS^{2}+SR^{2}) \\ \\ => 11^{2} + 17^{2} = 2(13^{2}+SR^{2}) \\ \\ => SR^{2} = 36 \\ \\ => SR = 6 \:units$

2) SInce,S is the mid -point of QR.

=> QR= 2*SR = 2*6 = 12 units

Answer 2

Answer:

QR=12

Step-by-step explanation:

In △PQR,

PQ=17 units,PR=11 units,QR=?,PS=13 units

Using Apollonius's theorem,

PQ 2 +PR 2=2(PS 2 +SR 2 )

17 2+11 2=2(13 2 +SR 2 )

289+121=2(169+SR 2 )

410=2(169+SR 2)

(169+SR 2)=205

SR 2 =36

SR=6 cm

Since S is the midpoint of QR

QR=2×SR

QR=12

QR=12 cm.

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