Question

The lengths of the sides of a triangle are 3, 3, 3V2. Can the triangle be a right triangle?

Answer 1

${\bold{\red{\huge{\mathbb{QUESTION}}}}}$

The lengths of the sides of a triangle are 3, 3, 3√2. Can the triangle be a right triangle?

$\bold{ \red{\star{\blue{TO \: \: PROVE }}}}$

IF ITS A RIGHT ANGLED OR NOT

$\bold{\blue{\star{\red{FORMULA}}}}$

IF IT WILL FOLLOW PYTHAGORAS THEOREM THEN IT WILL BE A RIGHT ANGLE TRIANGLE.

${HYPOTENUSE}^{2} \\ ={ PERPENDICULAR}^{2}+{BASE}^{2}$

$\bold{ \red{\star{\orange{GIVEN }}}}$

1ST SIDE -> 3

2ND SIDE -> 3

3RD SIDE ->3√2

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${HYPOTENUSE}^{2}\\ ={ PERPENDICULAR}^{2}+{BASE}^{2} \\{h}^{2}={p}^{2}+{b}^{2}$

AS HYPOTENUSE is always greater than other 2 sides so 3√2 can only be hypotenuse if it's a right angle triangle

${(3 \sqrt{2})}^{2} = {3}^{2} + {3}^{2} \\ 9 \times2 = 9 + 9 \\ 18 = 18$

${\red{\star}}{ \blue{HENCE \: PROVED}} { \red{ \star}}$

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