Question

Given by and vwz,what is the perimeter of the trapezoid WXYZ ..

Answer 1

We are given two similar triangles, therefore, we have the following relationship:

$\frac{VZ}{ZY}=\frac{VW}{WX}$

Solving for VW:

$VW=WX\times\frac{VZ}{ZY}$

Replacing in the equation:

$VW=36\times\frac{(44-27.5)}{27.5}$

Solving the operations:

$VW=21.6$

Now we use the Pythagorean theorem to determine the length of WZ, that is:

$WZ=\sqrt[]{(VW)^2-(VZ)^2}$

Replacing:

$WZ=\sqrt[]{(21.6)^2-(44-27.5)^2}$

Solving the operations:

$\begin{gathered} WZ=\sqrt[]{466.56-272.25} \\ WZ=\sqrt[]{194.31} \\ WZ=13.9 \end{gathered}$

Now we find XY using the following relationship:

$\frac{XY}{VY}=\frac{WZ}{VZ}$

Solving for XY:

$XY=VY\times\frac{WZ}{VZ}$

Replacing the values:

$XY=44\times\frac{13.9}{44-27.5}$

Solving the operations:

$XY=37.1$

The perimeter of the figure is:

$P=XW+WZ+ZY+XY$

Replacing:

$P=36+13.9+27.5+37.1$

Solving the operations:

$P=114.5$