Question

in the diagram below, ( overline{no} ) is parallel to ( overline{kl} ). if ( lo = 15 ), ( no = 24 ), and ( kl = 44 ), find the length of ( mo ). figures are not necessarily drawn to scale. state your answer in simplest radical form, if necessary.

Explanation:

Step1: Use the similarity of triangles

Since \( \overline{NO}\parallel\overline{KL}\), \(\triangle MNO\sim\triangle MKL\) (by AA similarity, as \(\angle M\) is common and \(\angle MON=\angle L = 90^{\circ}\)).
For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{MO}{ML}=\frac{NO}{KL}\). Let \(MO = x\), then \(ML=x + 15\).
Substituting the given values: \(\frac{x}{x + 15}=\frac{24}{44}\).

Step2: Cross - multiply and solve for \(x\)

Cross - multiplying gives \(44x=24(x + 15)\).
Expand the right - hand side: \(44x=24x+360\).
Subtract \(24x\) from both sides: \(44x-24x=24x + 360-24x\), so \(20x=360\).
Divide both sides by 20: \(x=\frac{360}{20}=18\).

Answer:

\(18\)