Question

Cu cat este egala aria unui triunghi cu laturile de 6 cm,5 cm si radical din 13 cm

Answer 1

$Folosim \: formula \: lui \: Heron$

$a = 6 \: cm$

$b = 5 \: cm$

$c = \sqrt{13} \: cm$

$A = \sqrt{p(p - a)(p - b)(p - c)}$

$p = \frac{a + b + c}{2} = \frac{6 + 5 + \sqrt{13} }{2} = \frac{11 + \sqrt{13} }{2}$

$A = \sqrt{ \frac{11 + \sqrt{13} }{2} ( \frac{11 + \sqrt{13} }{2} - 6)( \frac{11 + \sqrt{13} }{2} - 5)( \frac{11 + \sqrt{13} }{2} - \sqrt{13} )}$

$A = \sqrt{ \frac{11 + \sqrt{13} }{2} \times \frac{11 + \sqrt{13} - 12}{2} \times \frac{11 + \sqrt{13} - 10 }{2} \times \frac{11 + \sqrt{13} - 2 \sqrt{13} }{2} }$

$A = \sqrt{ \frac{11 + \sqrt{13} }{2} \times \frac{ \sqrt{13} - 1}{2} \times \frac{ \sqrt{13} + 1}{2} \times \frac{11 - \sqrt{13} }{2} }$

$A = \sqrt{ \frac{(11 + \sqrt{13})(11 - \sqrt{13} )( \sqrt{13} - 1)( \sqrt{13} + 1)}{2} }$

$A = \sqrt{ \frac{(121 - 13)(13 - 1)}{2} }$

$A = \sqrt{ \frac{108 \times 12}{2} }$

$A = \sqrt{108 \times 6}$

$A = \sqrt{648}$

$A = 18 \sqrt{2} \: {cm}^{2}$