Question

if the sides of a triangle is in ratio 3:4:5 prove that it is a right angled triangle​

Answer 1

Hence ABC is right angled triangle.

Hence ABC is right angled triangle.Step-by-step explanation:

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.Let ABC be the given triangle.

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.Let ABC be the given triangle.Let the sides be 3x,4x and hypotenuse be 5x.

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.Let ABC be the given triangle.Let the sides be 3x,4x and hypotenuse be 5x.According to Pythagoras theorem,

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.Let ABC be the given triangle.Let the sides be 3x,4x and hypotenuse be 5x.According to Pythagoras theorem,AC2=BC2+AB2

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.Let ABC be the given triangle.Let the sides be 3x,4x and hypotenuse be 5x.According to Pythagoras theorem,AC2=BC2+AB2BC2+AB2=(3x)2+(4x)2

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.Let ABC be the given triangle.Let the sides be 3x,4x and hypotenuse be 5x.According to Pythagoras theorem,AC2=BC2+AB2BC2+AB2=(3x)2+(4x)2=9x2+16x2=25x2

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.Let ABC be the given triangle.Let the sides be 3x,4x and hypotenuse be 5x.According to Pythagoras theorem,AC2=BC2+AB2BC2+AB2=(3x)2+(4x)2=9x2+16x2=25x2AC2=(5x)2=25x2

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.Let ABC be the given triangle.Let the sides be 3x,4x and hypotenuse be 5x.According to Pythagoras theorem,AC2=BC2+AB2BC2+AB2=(3x)2+(4x)2=9x2+16x2=25x2AC2=(5x)2=25x2AC2=BC2+AB2

Hence ABC is right angled triangle.Step-by-step explanation:Given the sides are in the ratio 3:4:5.Let ABC be the given triangle.Let the sides be 3x,4x and hypotenuse be 5x.According to Pythagoras theorem,AC2=BC2+AB2BC2+AB2=(3x)2+(4x)2=9x2+16x2=25x2AC2=(5x)2=25x2AC2=BC2+AB2Hence ABC is a right angled triangle.

Answer 2

Given :

• Ratio Of Sides = 3:4:5

To Prove:

The Triangle As A Right - Angled Triangle

Prove:-

$\bigstar$ Formula Used :

${\underline{\boxed{\red{\sf{A=\frac{H^{b }B }{2} }}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

Let, The Sides Of △ Be 3x,4x And 5x Cyclically

$\dashrightarrow \sf 5x>4x>3x$

According To The Pythagoras Theorem,

5x Is Hypotenuse (Longest Side)

3x/4x Can Be Perpendicular/Base

$\begin{gathered} \dashrightarrow \; \; \sf {\therefore (Hyp)^2=(Perp)^2+(Base)^2} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { (5x)^2+(3x)^2+(4x)^2 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 25x^2=8x^2+16x^2} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 25x^2=25x^2} \\ \end{gathered}$

$\begin{gathered} {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\orange{\frak{L.H.S=R.H.S }}}}}}}} \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

Therefore :

❛❛ Hence, It Is A Right Angled Triangle Proved❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$