In the diagram, HK is parallel to QR, PH = 4cm and HQ = 3cm. What is the ratio of KR:PR?

In the diagram, HK is parallel to QR, PH = 4cm and HQ = 3cm. What is the ratio of KR:PR?

Answer Details

Since HK is parallel to QR, angle HPQ is equal to angle KPR, and angle HQP is equal to angle KRP. Therefore, triangles HPQ and KRP are similar triangles by the angle-angle (AA) criterion. The ratio of the lengths of the corresponding sides of similar triangles is equal. Therefore: KR/PR = HQ/PQ = 3/(3+4) = 3/7 So the ratio of KR:PR is 3:7. Therefore, the correct option is 3:7.