Question

find the approximate side lengths and the perimeter of triangle uvw. if necessary, round your answers to the nearest hundredth.
the approximate length of side uv is
the approximate length of side vw is
the approximate length of side wu is
the approximate perimeter of triangle uvw is

Explanation:

Step1: Identify coordinates

Let \(U(-1,3)\), \(V(4,3)\), \(W(4, - 3)\).

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

For \(U(-1,3)\) and \(V(4,3)\), \(x_1=-1,y_1 = 3,x_2=4,y_2 = 3\). Then \(d_{UV}=\sqrt{(4-(-1))^2+(3 - 3)^2}=\sqrt{(4 + 1)^2+0^2}=\sqrt{25}=5\).

Step3: Use distance formula for side VW

For \(V(4,3)\) and \(W(4,-3)\), \(x_1 = 4,y_1=3,x_2 = 4,y_2=-3\). Then \(d_{VW}=\sqrt{(4 - 4)^2+(-3 - 3)^2}=\sqrt{0+(-6)^2}=\sqrt{36}=6\).

Step4: Use distance formula for side WU

For \(W(4,-3)\) and \(U(-1,3)\), \(x_1 = 4,y_1=-3,x_2=-1,y_2 = 3\). Then \(d_{WU}=\sqrt{(-1 - 4)^2+(3+3)^2}=\sqrt{(-5)^2+6^2}=\sqrt{25 + 36}=\sqrt{61}\approx 7.81\).

Step5: Calculate perimeter

Perimeter \(P=d_{UV}+d_{VW}+d_{WU}=5 + 6+7.81=18.81\).

Answer:

The approximate length of side UV is 5 units.
The approximate length of side VW is 6 units.
The approximate length of side WU is 7.81 units.
The approximate perimeter of triangle UVW is 18.81 units.