Respuesta :

jerichsen

Well, first you need to solve for s, or 1/2( a + b + c). The perimeter is 26 by adding all of them up. So half, or c, is 13. So now you do 13(13 -7)(13-9)(13-10). You get 13(6)(4)(3). Now multiply to get 13(72) to get 936. The square root of that is about 30.6. I might be wrong, but that is what I got.

[tex]\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=7\\ b=9\\ c=10\\ s=\frac{7+9+10}{2}\\[0.8em] \qquad 13 \end{cases} \\\\\\ A=\sqrt{13(13-7)(13-9)(13-10)}\implies A=\sqrt{13(6)(4)(3)} \\\\\\ A=\sqrt{936}~~ \begin{cases} 936=2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 13\\ \qquad 2^2\cdot 3^2\cdot 2\cdot 13\\ \qquad (2^2\cdot 3^2)\cdot 2\cdot 13\\ \qquad 6^2\cdot 26 \end{cases}\implies A=\sqrt{6^2\cdot 26}\implies A=6\sqrt{26}[/tex]

Otras preguntas