Chapter 5.5, Problem 3CE

To determine

To name: the isosceles trapezoid of the given figure and then to find its perimeter.

Answer to Problem 3CE

  $CXYB$ , 22

Explanation of Solution

Given information:

The given figure is shown below:

  

X, Y and Z are the midpoints of the isosceles triangle $ABC$ .

The isosceles trapezoid is a quadrilateral with one pair of parallel lines and one pair of

sides are of equal length.

Consider given figure,

X , Y and Z are the midpoints of $AC,AB$ and $BC$ respectively. So

  $\begin{array}{l}\overline{CX}=\frac{AC}{2}=\frac{10}{2}=5\\ \overline{BY}=\frac{AB}{2}=\frac{10}{2}=5\\ \overline{ZB}=\frac{BC}{2}=\frac{8}{2}=4\\ \Rightarrow \overline{CX}=\overline{BY}=\mathrm{5...........}(1)\end{array}$ .

  $XYZB$ is a parallelogram, so opposite sides are equal.

  $\begin{array}{l}XY\parallel ZB\parallel CB\\ \Rightarrow XY\parallel CB\\ XY=ZB=\mathrm{4.............}(2)\end{array}$

So, $CXYB$ has one pair of parallel lines and one pair of equal sides.

So $CXYB$ is the isosceles trapezoid..

Perimeterof trapezoid $CXYB$ is

  $\begin{array}{l}=CX+XY+BY+BC\\ =5+4+5+8\\ =22\end{array}$

Hence, $CXYB$ is the isosceles trapezoid and its perimeter $=22$ .