Question

using the provided image, what is the ratio of rq to rp? 1.500 0.832 0.667 0.555

Explanation:

Step1: Identify Similar Triangles

Triangles \( \triangle LMN\), \( \triangle RQP\), and \( \triangle DEF\) are similar (by AA similarity as they have right - angles and equal non - right angles).

Step2: Use Proportional Sides

For similar triangles, the ratios of corresponding sides are equal. Given \(\frac{QP}{RP}=0.555\). Since \(RQ\) and \(QP\) are corresponding sides (in the context of similar triangles where the ratio of sides is considered based on the angle - side relationships in right - angled similar triangles), the ratio of \(RQ\) to \(RP\) is the same as the ratio of \(QP\) to \(RP\) (because of the similarity and side - angle - side correspondence in similar right - angled triangles). So, \(\frac{RQ}{RP}=\frac{QP}{RP}\) (by the property of similar triangles that corresponding side ratios are equal).

Answer:

D. \(0.555\)