Question

In triangle PQR,point S is a midpoint of side QR.If PQ = 11 ,PR=17,PS =13, find QR

Answer 1

this should help yeah?

Answer 2

Answer-

QR = 12 units

Solution-

According to Apollonius's Theorem,

$b^2+c^2=\frac{a^2}{2} +2d^2$

Comparing the attached triangle, with the given triangle,

PQ = 11,

PR = 17,

PS = 13

Applying Apollonius's Theorem,

$\Rightarrow PQ^{2}+PR^{2}=\frac{QR^2}{2}+2PS^2\\\\\Rightarrow (11)^{2}+(17)^{2}=\frac{QR^2}{2}+2(13)^2\\\\\Rightarrow QR^{2} = 2(11^2+17^2-2(13)^2)\\\\\Rightarrow QR^{2} = 2(121+289-338)=2\times 72\\\\\Rightarrow QR^{2} = 144\\\\\Rightarrow QR=12$

Therefore, the value of QR is 12