Question

I need help with number 8

Answer 1

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

Answer 2

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.