Question

select the correct answer from each drop - down menu. 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 units. the approximate length of side vw is units. the approximate length of side wu is units. the approximate perimeter of triangle uvw is units.

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 \(UV\)

For points \(U(-1,3)\) 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 \(VW\)

For points \(V(4,3)\) 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 \(WU\)

For points \(W(4,-3)\) 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 \(P\)

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

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.