Question

what is the best approximation for the perimeter of the pentagon abcde? 25 units 17 units 22 units 54 units

Explanation:

Step1: Find the length of each side using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

• For \(EA\): \(E(0,0)\), \(A(3,4)\)

\(EA=\sqrt{(3 - 0)^2+(4 - 0)^2}=\sqrt{9 + 16}=\sqrt{25}=5\)

• For \(AB\): \(A(3,4)\), \(B(6,3)\)

\(AB=\sqrt{(6 - 3)^2+(3 - 4)^2}=\sqrt{9+1}=\sqrt{10}\approx3.16\)

• For \(BC\): \(B(6,3)\), \(C(8,0)\)

\(BC=\sqrt{(8 - 6)^2+(0 - 3)^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.61\)

• For \(CD\): \(C(8,0)\), \(D(2,-3)\)

\(CD=\sqrt{(2 - 8)^2+(-3 - 0)^2}=\sqrt{36+9}=\sqrt{45}\approx6.71\)

• For \(DE\): \(D(2,-3)\), \(E(0,0)\)

\(DE=\sqrt{(0 - 2)^2+(0+3)^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.61\)

Step2: Sum up the lengths of all sides

\(P=EA + AB+BC + CD+DE\)
\(P\approx5+3.16 + 3.61+6.71+3.61\)
\(P\approx22\)

Answer:

22 units