Question

In Parallelogram Lane, VW is perpendicular to En and NX is perpendicular to LE. Find the measure If EN is 18 cm, VW is 6cm And LE is 9 cm, Find Nx

Answer 1

1) build LM || WV ( therefore $\angle$ LME=90)

2) suppose $\angle XNE = \alpha \Rightarrow \angle XEN = \angle LEM = (90 - \angle XNE) = 90 - \alpha$ (from the triangle XEN)

3) From the triangle LME:

$\angle MLE = (90 - \angle MEL) = 90 - (90 - \alpha) = \alpha$

4) From the triangles XEN and LME:

$\cos(\alpha) = \mathrm{XN} / \mathrm{EN} = \mathrm{LE} / \mathrm{LM}$

5) LM = WV (because WLMV – is a rectangle)

6) XN/EN = LE/WV $\Rightarrow$ XN = EN * (LE/WV) = 18 * (6/9) = 12

Answer: XN=12