Question

If KJ = 33 and KN = sqrt{10} " align="absmiddle" class="latex-formula"> , calculate the length of GJ.
1. 27
2. $6\sqrt{161}$
3. $3\sqrt{161}$
4. 54
also please show work on how you found your answer

Answer 1

KJ is the hypotenuse of the right triangle KJN, therefore:KJ^2 = KN^2 + JN^233^2 = (6sqrt10)^2 + JN^21089 = 360 + JN^2JN^2 = 729JN = 27
The figure is a trapezoid, since GH // JI, and MN is perpendicular to HI. Therefore GN = JN = 27. The length of GJ = 54.