Question

the edges of a triangular board are 12 CM, 16 cm and 20 CM. then find the cost of painting the board @ 15paise per centimetre square

Answer 1

$the \: three \: sides \: of \: the \: triangle \: are \: 12cm \: 13cm \: 20cm \\ area \: of \: the \: triangle = \frac{1}{2} \times base \times height \\ base = 20cm \\ height = {oc}^{2} + {ob}^{2} = {bc}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {10}^{2} + {ob}^{2} = {16 }^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: \: \: \: \: \: \: \: ob \: = \sqrt{156} \\ area \: of \: the \: triangle = \frac{1}{2} \times base \times height \: \\ = \frac{1}{2} \times 20 \times \sqrt{156} \\ = 10 \sqrt{156} \\ = 10 \times 2 \sqrt{39} \\ = 20 \sqrt{39}cm \\ \\ the \: painting \: cost = 0.15 \times 20 \sqrt{39} \\ = \frac{15}{100} \times 2 \sqrt{39} \\ = 6 \sqrt{39}$
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