Question

what is the perimeter of (\triangle efg)?
write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Find coordinates of points

Coordinates: \(E(-10,3)\), \(F(3,9)\), \(G(1,-2)\)

Step2: Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For \(EF\):
\(x_1=-10,y_1 = 3,x_2=3,y_2 = 9\)
\(EF=\sqrt{(3-(-10))^2+(9 - 3)^2}=\sqrt{13^2+6^2}=\sqrt{169 + 36}=\sqrt{205}\approx14.3\)
For \(FG\):
\(x_1=3,y_1 = 9,x_2=1,y_2=-2\)
\(FG=\sqrt{(1 - 3)^2+(-2 - 9)^2}=\sqrt{(-2)^2+(-11)^2}=\sqrt{4+121}=\sqrt{125}\approx11.2\)
For \(EG\):
\(x_1=-10,y_1 = 3,x_2=1,y_2=-2\)
\(EG=\sqrt{(1-(-10))^2+(-2 - 3)^2}=\sqrt{11^2+(-5)^2}=\sqrt{121+25}=\sqrt{146}\approx12.1\)

Step3: Calculate perimeter

Perimeter \(P=EF + FG+EG\)
\(P\approx14.3+11.2 + 12.1\)

Answer:

\(37.6\)