Question

what is the perimeter of △ijk? write your answer as an integer or as a decimal rounded to the nearest tenth. perimeter = units

Explanation:

Step1: Find the coordinates of the vertices

From the graph, \(I(-8, - 2)\), \(J(0,10)\), \(K(8,-2)\)

Step2: Calculate the length of \(IJ\) using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

\(d_{IJ}=\sqrt{(0 + 8)^2+(10 + 2)^2}=\sqrt{64 + 144}=\sqrt{208}=4\sqrt{13}\approx14.4\)

Step3: Calculate the length of \(JK\) using the distance formula

\(d_{JK}=\sqrt{(8 - 0)^2+(-2 - 10)^2}=\sqrt{64+144}=\sqrt{208}=4\sqrt{13}\approx14.4\)

Step4: Calculate the length of \(IK\)

The \(y -\)coordinates of \(I\) and \(K\) are the same. So \(d_{IK}=\vert8-(-8)\vert = 16\)

Step5: Calculate the perimeter \(P\)

\(P=d_{IJ}+d_{JK}+d_{IK}\approx14.4 + 14.4+16=44.8\)

Answer:

\(44.8\)