Question

the hypotenuse of a right triangle is 1 metre less than twice the smaller side. if the trird side is 1 metre more than the smaller side. find the side of of the triangle.?​

Answer 1

Step-by-step explanation:

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$\Large\bf{\underbrace{\underline{Question:-}}}$

:$\Longrightarrow$ The hypotenuse of a right triangle is 1 metre less than twice the smaller side. if the trird side is 1 metre more than the smaller side. find the side of of the triangle?

$\Large\bf{\underbrace{\underline{To\ find:-}}}$

:$\Longrightarrow$ We have to find the sides of the triangle.

$\Large\bf{\underbrace{\underline{Solution:-}}}$

:$\Longrightarrow$ Let the shortest side of the right triangle be x m.

:$\Longrightarrow$ Then:-

:$\Longrightarrow$ $\sf{Hypotenuse\ =\ (2x\ -\ 1)\ m.}$

:$\Longrightarrow$ $\sf{And\ third\ side\ =\ (x\ +\ 1)\ m.}$

$\large\bf{\underbrace{\underline{Using\ Pythagoras\ Theorem:-}}}$

:$\Longrightarrow$ $\sf{Hypotenuse²\ =\ (Side1)²\ +\ (Side2)²}$

:$\Longrightarrow$ $\sf{(2x\ -\ 1)²\ =\ x²\ +\ (x\ +\ 1)²}$

:$\Longrightarrow$ $\sf{4x²\ -\ 4x\ +\ 1\ =\ x²\ +\ 2x\ +\ 1}$

:$\Longrightarrow$ $\sf{4x²\ -\ 4x\ +\ 1\ =\ 2x²\ +\ 2x\ 1}$

:$\Longrightarrow$ $\sf{4x²\ -\ 2x²\ -\ 4x\ -\ 2x\ +\ 1\ -\ 1\ =\ 0}$

:$\Longrightarrow$ $\sf{2x²\ -\ 6x\ =\ 0}$

:$\Longrightarrow$ $\sf{2x\ (x\ -\ 3)\ =\ 0}$

:$\Longrightarrow$ $\sf{2x\ =\ 0\ or\ x\ -\ 3\ =\ 0}$

:$\Longrightarrow$ $\sf{x\ =\ 0\ or\ x\ =\ 3}$

:$\Longrightarrow$ $\sf{x\ =\ 3}$

:$\Longrightarrow$ (By rejecting x = 0 , Since, side cannot be 0)

:$\Longrightarrow$ $\sf{Thus,\ x\ =\ 3}$

:$\Longrightarrow$ $\sf{2x\ -\ 1\ =\ 2(3)\ -\ 1\ =\ 5}$.....(Hypotenuse)

:$\Longrightarrow$ $\sf{x\ +\ 1\ =\ 3\ +\ 1\ =\ 4}$.....(Third side)

Hence:-

● The sides of given right angled triangle are 3m, 4m, and 5m.

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