Question

what is the perimeter of the triangle to the nearest unit?

Explanation:

Step1: Find coordinates of points

Assume \(A(4,6)\), \(B(8,1)\), \(C(4, - 9)\)

Step2: Calculate length of \(AB\)

Use distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
For \(A(4,6)\) and \(B(8,1)\):
\(AB=\sqrt{(8 - 4)^2+(1 - 6)^2}=\sqrt{4^2+( - 5)^2}=\sqrt{16 + 25}=\sqrt{41}\approx6.4\)

Step3: Calculate length of \(BC\)

For \(B(8,1)\) and \(C(4, - 9)\):
\(BC=\sqrt{(4 - 8)^2+( - 9 - 1)^2}=\sqrt{( - 4)^2+( - 10)^2}=\sqrt{16 + 100}=\sqrt{116}\approx10.8\)

Step4: Calculate length of \(AC\)

For \(A(4,6)\) and \(C(4, - 9)\):
\(AC=\sqrt{(4 - 4)^2+( - 9 - 6)^2}=\sqrt{0+( - 15)^2}=15\)

Step5: Calculate perimeter

Perimeter \(P = AB+BC + AC\approx6.4+10.8+15 = 32.2\approx32\)

Answer:

\(32\)