Question

Which of the following can be the sides of a right triangle?
(a) 2.5 cm, 6.5 cm, 6 cm
(b) 2 cm, 2 cm, 5 cm
(c) 1.5 cm, 2 cm, 2.5 cm
Both (a) and (c)

Answer 1

$\huge {\boxed {\mathbb {QUESTION}}}$

Which of the following can be the sides of a right triangle?

(a) 2.5 cm, 6.5 cm, 6 cm

(b) 2 cm, 2 cm, 5 cm

(c) 1.5 cm, 2 cm, 2.5 cm

Both (a) and (c)

$\huge {\boxed {\mathbb {ANSWER}}}$

$Square\: of \:the\: largest\: side\: is \:equal\: to\: the\\ sum\: of \:the\: squares\: of\: other\: two\: sides\: then\: it\\ is\: a \:right\: angled\: triangle$

$\huge {(a) 2.5 cm, 6.5 cm, 6 cm}$

$Largest\: side=6.5cm$

$Other\: two \:sides =2.5cm,6cm$

$\implies {(6.5)}^{2}={(2.5)}^{2}+{(6)}^{2}$

$\implies 42.25=6.25+36$

$\implies{\boxed{\boxed {42.25=42.25}}}$

$\therefore 2.5 cm, 6.5 cm, 6 cm\: becomes\: right \:angled\: triangle$

_________________________________________

$\huge {(b) 2 cm, 2 cm, 5 cm}$

$Largest\: side=5cm$

$Other\: two \:sides =2cm,2cm$

$\implies {(5)}^{2}={(2)}^{2}+{(2)}^{2}$

$\implies 25=4+4$

$\implies{\boxed{\boxed {25 \cancel{=}8}}}$

$\therefore 2 cm, 2 cm, 5 cm\:doesn't \: becomes\: right \:angled\: triangle$

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$\huge {(c) 1.5 cm, 2 cm, 2.5 cm}$

$Largest\: side=2.5cm$

$Other\: two \:sides =1.5cm,2cm$

$\implies {(2.5)}^{2}={(1.5)}^{2}+{(2)}^{2}$

$\implies 6.25=2.25+4$

$\implies{\boxed{\boxed {6.25=6.25}}}$

$\therefore 2 cm, 2 cm, 5 cm \: becomes\: right \:angled\: triangle$

_________________________________________

Which of the following can be the sides of a right triangle?

${\boxed {(a) 2.5 cm, 6.5 cm, 6 cm✅}}$

${\boxed {(b) 2 cm, 2 cm, 5 cm❌}}$

${\boxed {(c) 1.5 cm, 2 cm, 2.5 cm✅}}$

${\boxed {(d) Both (a) and (c)✅}}$

$\therefore Option\: (d) \:is\: correct$

$\huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU }}}$

_________________________________________

$\huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$Properties\: of \:right\: angled\: triangle$

• $One\: angle\: is \:always \:{90}^{\circ} \:or\: right \:angle.$
• $The\: side\: opposite\: angle\: {90}^{\circ} \:is \:the\\ hypotenuse.$
• $The\: hypotenuse\: is\: always\: the\: longest\\ side.$
• $The\: sum\: of\: the\: other\: two\: interior\: angles\: is \:\\equal to {90}^{\circ} .$
• $The\: other\: two\: sides\: adjacent\: to\: the\\ right\: angle\: are\: called\: base\: and\\perpendicular.$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$

Answer 2

Answer:

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