Question

what is the perimeter of triangle def? round your answer to the nearest hundredth. > enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Find coordinates of points

Let \(D(-3,5)\), \(E(1,1)\), \(F(-4,3)\)

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

\(DE=\sqrt{(1-(-3))^2+(1 - 5)^2}=\sqrt{(4)^2+(-4)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.66\)

Step3: Use distance formula for \(EF\)

\(EF=\sqrt{(-4 - 1)^2+(3 - 1)^2}=\sqrt{(-5)^2+(2)^2}=\sqrt{25+4}=\sqrt{29}\approx5.39\)

Step4: Use distance formula for \(DF\)

\(DF=\sqrt{(-4-(-3))^2+(3 - 5)^2}=\sqrt{(-1)^2+(-2)^2}=\sqrt{1 + 4}=\sqrt{5}\approx2.24\)

Step5: Calculate perimeter

\(P=DE + EF+DF\approx5.66+5.39+2.24 = 13.29\)

Answer:

13.29