Question

Aria unui triunghi cu lungimile laturilor de 7cm,24cm,respectiv 25cm,este cu...

Answer 1

Folosim formula lui Heron :

$a = 7 \: cm$

$b = 24 \: cm$

$c = 25 \: cm$

$p = \frac{a + b + c}{2}$

$p = \frac{7 + 24 + 25}{2}$

$p = \frac{56}{2}$

$p = 28\:cm$

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

$A = \sqrt{28(28 - 7)(28 - 24)(28 - 25)}$

$A = \sqrt{28 \times 21 \times 4 \times 3}$

$A = \sqrt{28} \times \sqrt{21} \times \sqrt{4} \times \sqrt{3}$

$A = 2 \sqrt{7} \times \sqrt{21} \times 2 \times \sqrt{3}$

$A = 4 \sqrt{7 \times 3 \times 21}$

$A = 4 \sqrt{21 \times 21}$

$A = 4 \times 21$

$A = 84 \: {cm}^{2}$