Math, asked by lalujohn1977, 4 months ago

pQr is a triangle right angled at oif Q =5cmand pr=12lcm find qr​

Answers

Answered by Anonymous
39

Correct Question

  • PQR is a triangle right angled at P, if PQ = 5cm and PR = 12cm then find QR.

Given

  • In a right angled triangle PQR :-
  • PQ = Base = 5cm
  • PR = Perpendicular = 12cm

To find

  • Length of QR (Hypotenuse).

Solution

  • As it is given in the question that the given triangle is a right angled triangle.
  • Let the hypotenuse be x cm.

⠀⠀⠀⠀⠀\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf 12cm}\put(2.8,.3){\large\bf 5cm}\put(4.3,2.5){\large\bf $\ x $}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\end{picture}

⠀⠀⠀⠀⠀⠀⠀⠀Required Diagram

  • Using Pythagoras theorem

\large{\boxed{\boxed{\sf{(QR)^2 = (PQ)^2 + (PR)^2}}}}

\tt:\implies\: \: \: \: \: \: \: \: {QR^2 = (5)^2 + (12)^2}

\tt:\implies\: \: \: \: \: \: \: \: {QR^2 = 25 + 144}

\tt:\implies\: \: \: \: \: \: \: \: {QR^2 = 169 }

\tt:\implies\: \: \: \: \: \: \: \: {QR = \sqrt{169}}

\bf:\implies\: \: \: \: \: \: \: \: {QR = 13}

Hence,

  • PQ (hypotenuse) is 13 cm long.

━━━━━━━━━━━━━━━━━━━━━━

Similar questions