$\begin{aligned}56.\quad&\textrm{Perhatikan gambar berikut}\end{aligned}$.
$\begin{aligned}\quad\qquad&\textrm{Jika PQ}=6\:\: \textrm{cm dan PR}=8\:\: \textrm{cm, maka panjang}\\ &\textrm{jari-jari lingkaran dalam}\:\: \bigtriangleup PQR=\:....\\ &\textrm{a}.\quad 1\:\:\textrm{cm}\\ &\textrm{b}.\quad 2\:\:\textrm{cm}\\ &\textrm{c}.\quad 2,5\:\:\textrm{cm}\\ &\textrm{d}.\quad 3\:\:\textrm{cm}\\\\ &\textrm{Jawab}:\quad \textbf{b}\\ &\textrm{Cukup jelas bahwa panjang RQ}=10\:\: \textrm{cm}\\ &\textrm{Sehingga panjang jari-jari lingkran dalamnya}:\\ &r_{dalam}=\displaystyle \frac{\left[ PQR \right]}{s}=\frac{\left[ PQR \right]}{\displaystyle \frac{p+q+r}{2}}=\frac{2\left[ PQR \right]}{p+q+r}\\ &\:\:\:\,\quad\quad=\displaystyle \frac{2\left( \displaystyle \frac{1}{2}.6.8 \right)}{6+8+10}=\frac{48}{24}=2\:\: \textrm{cm} \end{aligned}$.
$\begin{aligned}57.\quad&\textrm{Perhatikan gambar berikut}\end{aligned}$.
$\begin{aligned}\quad\qquad&\textrm{Berdasar gambar di atas, luas}\:\: \bigtriangleup BOC=\:....\\ &\textrm{a}.\quad 10\:\:\textrm{cm}^{\displaystyle 2}\\ &\textrm{b}.\quad 12\:\:\textrm{cm}^{\displaystyle 2}\\ &\textrm{c}.\quad 13\:\:\textrm{cm}^{\displaystyle 2}\\ &\textrm{d}.\quad 14\:\:\textrm{cm}^{\displaystyle 2}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Cukup jelas bahwa panjang BC}=13\:\: \textrm{cm}\\ &\textrm{Sehingga panjang jari-jari lingkran dalamnya}:\\ &r_{dalam}=\displaystyle \frac{\left[ ABC \right]}{s}=\frac{\left[ ABC \right]}{\displaystyle \frac{a+b+c}{2}}=\frac{2\left[ ABC \right]}{a+b+c}\\ &\:\:\:\,\quad\quad=\displaystyle \frac{2\left( \displaystyle \frac{1}{2}.5.12 \right)}{5+12+13}=\frac{60}{30}=2\:\: \textrm{cm}\\ &\textrm{Selanjutnya untuk luas}\: \bigtriangleup BOC\\ &=\displaystyle \frac{1}{2}\times \textrm{alas}\times \textrm{tinggi}=\displaystyle \frac{1}{2}.13.2=13\:\: \textrm{cm}^{\displaystyle 2} \end{aligned}$.
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