Question

the vertices of triangle rst are listed below.
r(-8,6), s(40,6), t(16,-4)
what is the perimeter of triangle rst?
a. 240 units
b. 74 units
c. 100 units
d. 156 units

Explanation:

Step1: Calculate the length of \(RS\)

Since \(R(-8,6)\) and \(S(40,6)\) have the same \(y -\)coordinate, use the distance formula \(d=\vert x_2 - x_1\vert\).
\(RS=\vert40-(-8)\vert=\vert40 + 8\vert=48\)

Step2: Calculate the length of \(ST\)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \(S(40,6)\) and \(T(16,-4)\)
\(ST=\sqrt{(16 - 40)^2+(-4 - 6)^2}=\sqrt{(-24)^2+(-10)^2}=\sqrt{576 + 100}=\sqrt{676}=26\)

Step3: Calculate the length of \(RT\)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \(R(-8,6)\) and \(T(16,-4)\)
\(RT=\sqrt{(16-(-8))^2+(-4 - 6)^2}=\sqrt{(24)^2+(-10)^2}=\sqrt{576+100}=\sqrt{676}=26\)

Step4: Calculate the perimeter \(P\)

\(P=RS + ST+RT\)
\(P=48+26 + 26\)
\(P = 100\)

Answer:

C. 100 units