Question

1. multiple choice 1 point

given: wy = 2 units, cy = 5 units, ym = 8 units, mg = 10 units, and gx = 13 units
select the true statement below.
hx = 9.2 units
hx = 15.2 units
hx = 14.8 units
hx = 13.2 units
hx = 12 units
hx = 14.4 units

Explanation:

Step1: Identify similar triangles

Since \(WY\perp CX\), \(RM\perp CX\), \(NG\perp CX\), \(HX\perp CX\), we have \(\triangle CWY\sim\triangle CRM\sim\triangle CNG\sim\triangle CHX\) (by AA similarity criterion as all right - angled and share the same angle at \(C\)).

Step2: Use the ratio of sides in similar triangles

For \(\triangle CWY\) and \(\triangle CHX\), the ratio of the sides is based on the lengths of the segments on \(CX\).
\(CY = 5\) units, \(CX=CY + YM+MG + GX=5 + 8+10 + 13=36\) units, and \(WY = 2\) units.
Let \(HX = h\). Using the property of similar triangles \(\frac{WY}{HX}=\frac{CY}{CX}\).

Step3: Substitute the values

Substitute \(WY = 2\), \(CY = 5\), and \(CX = 36\) into \(\frac{WY}{HX}=\frac{CY}{CX}\), we get \(\frac{2}{h}=\frac{5}{36}\). Cross - multiply: \(5h=2\times36\), so \(h=\frac{72}{5}=14.4\)

Answer:

HX = 14.4 units