Question

9. What is the length of XY if the quadrilateral is an isosceles trapezoid?y+1W12XYy+6Z

Answer 1

XY = 7

Step-by-step explanation:

We are given the isosceles trapezoid WXYZ

`\begin{gathered} WX=12 \\ XY=y+1 \\ YZ=y+6 \\ WZ=? \end{gathered}`

One of the properties of an isosceles trapezoid is that "the non-parallel sides (legs) are congruent"

Mathematically,

`\begin{gathered} WX\cong YZ \\ \Rightarrow12=y+6 \\ 12=y+6 \\ \text{Subtract ''6'' from both sides, we have:} \\ 12-6=y \\ 6=y \\ y=6 \end{gathered}`

We will proceed to obtain length XY as shown below:

`\begin{gathered} XY=y+1 \\ but:y=6 \\ XY=6+1 \\ XY=7 \\ \\ \therefore XY=7 \end{gathered}`

Therefore, the length of XY equals 7. The answer is the first option