Answer :
[tex]M=(4,-3)\qquad D=(-6,-1)\qquad T=(7,-8)\\\\\\
|MD|=\sqrt{\big(-6-4\big)^2+\big(-1-(-3)\big)^2}=\sqrt{\big(-10\big)^2+\big(-1+3\big)^2}=\\\\=\sqrt{100+2^2}=\sqrt{104}\approx\boxed{10.2}\\\\\\\\
|DT|=\sqrt{\big(7-(-6)\big)^2+\big(-8-(-1)\big)^2}=\sqrt{\big(7+6\big)^2+\big(-8+1\big)^2}=\\\\=\sqrt{13^2+(-7)^2}=\sqrt{169+49}=\sqrt{218}\approx\boxed{14.8}\\\\[/tex]
[tex]|TM|=\sqrt{\big(4-7\big)^2+\big(-3-(-8)\big)^2}=\sqrt{\big(-3\big)^2+\big(-3+8\big)^2}=\\\\=\sqrt{9+5^2}=\sqrt{9+25}=\sqrt{34}\approx\boxed{5.8}[/tex]
So the perimeter:
[tex]P_{\Delta MDT}=|MD|+|DT|+|TM|\approx10.2+14.8+5.8=\boxed{30.8}[/tex]
Answer C.
|MD|=\sqrt{\big(-6-4\big)^2+\big(-1-(-3)\big)^2}=\sqrt{\big(-10\big)^2+\big(-1+3\big)^2}=\\\\=\sqrt{100+2^2}=\sqrt{104}\approx\boxed{10.2}\\\\\\\\
|DT|=\sqrt{\big(7-(-6)\big)^2+\big(-8-(-1)\big)^2}=\sqrt{\big(7+6\big)^2+\big(-8+1\big)^2}=\\\\=\sqrt{13^2+(-7)^2}=\sqrt{169+49}=\sqrt{218}\approx\boxed{14.8}\\\\[/tex]
[tex]|TM|=\sqrt{\big(4-7\big)^2+\big(-3-(-8)\big)^2}=\sqrt{\big(-3\big)^2+\big(-3+8\big)^2}=\\\\=\sqrt{9+5^2}=\sqrt{9+25}=\sqrt{34}\approx\boxed{5.8}[/tex]
So the perimeter:
[tex]P_{\Delta MDT}=|MD|+|DT|+|TM|\approx10.2+14.8+5.8=\boxed{30.8}[/tex]
Answer C.
