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Home » 1. If the sides of a triangle are     long, determine whether the triangle is a right-angled triangle.
1. If the sides of a triangle are

    \[\mathbf{3}\text{ }\mathbf{cm},\text{ }\mathbf{4}\text{ }\mathbf{cm},\text{ }\mathbf{and}\text{ }\mathbf{6}\text{ }\mathbf{cm}\]

long, determine whether the triangle is a right-angled triangle.
CBSE | Class 10 | Maths | RD Sharma | Triangles
1. If the sides of a triangle are

    \[\mathbf{3}\text{ }\mathbf{cm},\text{ }\mathbf{4}\text{ }\mathbf{cm},\text{ }\mathbf{and}\text{ }\mathbf{6}\text{ }\mathbf{cm}\]

long, determine whether the triangle is a right-angled triangle.

Solution:

We have,

Sides of triangle as

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> AB\text{ }=\text{ }3\text{ }cm \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> BC\text{ }=\text{ }4\text{ }cm \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> AC\text{ }=\text{ }6\text{ }cm \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

                                                        

    \[\]

On finding their squares, we get

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> A{{B}^{2}}~=\text{ }{{3}^{2}}~=\text{ }9 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> B{{C}^{2~}}=\text{ }{{4}^{2}}~=\text{ }16 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> A{{C}^{2}}~=\text{ }{{6}^{2}}~=\text{ }36 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> Since,\text{ }A{{B}^{2}}~+\text{ }B{{C}^{2}}~\ne \text{ }A{{C}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

                                                          

So, by converse of Pythagoras theorem the given sides cannot be the sides of a right triangle.

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