Question

in Δ PQR if angle Q is 90 degree , PQ= 8cm , QR = 15cm and QS is median Find QS

Answer 1

Answer:

$\huge\bold\red{ANSWER}$

Step-by-step explanation:

$\large{\underline{\rm{\red{SOLUTION :}}}}$

$\implies \sf \blue{by\:using\:hypotenuse\:we\:can\:find\:PR}\\ \implies \sf \blue{(PQ)^2+(QR)^2=(PR)^2}\\ \implies \sf \blue {8^2+15^2=(PR)^2}\\ \implies \sf \blue{PR=17}\\ \implies \sf \blue {S \:is \:midpoint\:of\:PR}$

$\implies \sf \blue{T\:is \:midpoint\:of\:PQ}\\ \implies \sf \blue{PT\: is\:4cm}\\ \implies \sf \blue{(PT)^2+(TS)^2=(PS)^2}\\ \implies \sf \blue {4^2+(TS)^2=(8.5)^2}\\ \implies \sf \blue {(TS)^2=72.25-16}\\ \implies \sf \blue {TS=7.5}\\ \implies \sf \blue {\triangle TSQ\: is\: a\:right \:angle\:so}\\ \implies \sf \blue {(7.5)^2+4^2=(QS)^2}\\ \implies \sf \blue {QS=72.25\:is\:your\:answer}$

Answer 2

Answer:

byusinghypotenusewecanfindPR⟹(PQ)

2+(QR) 2 =(PR) 2

⟹8 2 +15 2 =(PR) 2

⟹PR=17

⟹SismidpointofPR

$\begin{gathered}\implies \sf \blue{T\:is \:midpoint\:of\:PQ}\\ \implies \sf \blue{PT\: is\:4cm}\\ \implies \sf \blue{(PT)^2+(TS)^2=(PS)^2}\\ \implies \sf \blue {4^2+(TS)^2=(8.5)^2}\\ \implies \sf \blue {(TS)^2=72.25-16}\\ \implies \sf \blue {TS=7.5}\\ \implies \sf \blue {\triangle TSQ\: is\: a\:right \:angle\:so}\\ \implies \sf \blue {(7.5)^2+4^2=(QS)^2}\\ \implies \sf \blue {QS=72.25\:is\:your\:answer}\end{gathered}$