Question

2 Verify if the following are the sides of a
right triangle. If it is a right triangle, then
find the hypotenuse.
(i) 12 cm, 10 cm and 8 cm
(ii) 15 cm, 36 cm and 39 cm​

Answer 1

Answer:

hypotenuse is the greatest side so

$i)12cm \: is \: the \: hypotenuse \\ means \: \sqrt{ {10}^{2} + {8}^{2} } = 12 \\ \sqrt{100 + 64} = 12 \\ \sqrt{ 164} = 12 \\ \\ root \: 164\: is \: not \: equal \: to \: 12 \\ so \: it \: is \: not \: a \: right \: angle \: triangle$

$ii)39cm \: is \: the \: hypotenuse \\ means \sqrt{ {15}^{2} + {36}^{2} } = 39 \\ \sqrt{225 + 1296} = 39 \\ 39 = 39 \\ so \: it \: is \: a \: right \: angle \: triangle$

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