[tex]a = 4\\
b = 5\\
c = 7\\
p=\frac{4+5+7}2=\frac{16}2=8\\
\\
P=\sqrt{p(p-a)(p-b)(p-c)}\\
\\
P=\sqrt{8(8-4)(8-5)(8-7)}=\sqrt{8*4*3*1}=\sqrt{96}=\sqrt{16*6}=4\sqrt6\\
\\
P=\frac{a*h_1}2 = \frac{b*h_2}2=\frac{c*h_3}2\\
\\
4\sqrt6=\frac{4*h_1}2 /*2\\
8\sqrt6=4*h_1 /:4\\
2\sqrt6=h_1\\
\\
4\sqrt6=\frac{5*h_2}2 /*2\\
8\sqrt6=5*h_2 /:5\\
\frac{8\sqrt6}5=h_2\\
\\
4\sqrt6=\frac{7*h_3}2 /*2\\
8\sqrt6=7*h_3 /:7\\
\frac{8\sqrt6}7=h_3[/tex]
