Question

determine whether the triangle whose lengths of sides are 3cm 4cm 5cm is a right - angled triangle

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Sides of triangle are 3cm, 4cm, 5cm}$

$\underline{\textbf{To find:}}$

$\textsf{Whether the given triangle is right angled or not}$

$\underline{\textbf{Solution:}}$

$\textsf{We apply Converse of Pythagoras theorem to}$

$\textsf{solve the problem}$

$\underline{\textbf{Converse of Pythagoras theorem:}}$

$\textbf{If sum of the squares of any two sides of a triangle}$

$\textbf{is equal to square of the third side, then the}$

$\textbf{angle contained by these two sides is right angle}$

$\mathsf{Let\;a=3\,cm,\;b=4\,cm,\;c=5\,cm}$

$\mathsf{a^2+b^2}$

$\mathsf{=3^2+4^2}$

$\mathsf{=9+16}$

$\mathsf{=25}$

$\mathsf{=c^2}$

$\implies\mathsf{a^2+b^2=c^2}$

$\textsf{By Converse of Pythagoras theorem,}$

$\textsf{The triangle with given lengths is a right angled triangle}$

$\underline{\textbf{Find more:}}$

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Answer 2

Step-by-step explanation:

the size of a triangle are 3 cm 4 cm and 5 cm determine whether it is a right triangle