Question

I need help solving this

Answer 1

The length of GH is 70 units.

Explanation:

It is given that, Q is circumcenter of triangle GHJ.

This means that, GQ = QH = JQ

given that, GQ = 15x - 23 and JQ = 9x + 1

thus,
`15x - 23 = 9x + 1`

`6x = 24` , x = 4 units.

Thus, GQ = QH = JQ = 9(4) + 1 = 37 units

QN is perpendicular to line GH.

Thus in right angled triangle QNH,

`(HN)^(2) + (12)^(2) = 37^(2)`

HN =
`√(1225)` = 35 units.

Triangles, QGN and QHN are congruent, thus GN = HN = 35 units

The length of GH = (2)(35) = 70 units.