In the diagram, ?XYZ is similar to ?PRQ, |XY| = 5cm, |XZ| =3.5cm and |PR| = 8cm. Find |PQ|

In the diagram, ?XYZ is similar to ?PRQ, |XY| = 5cm, |XZ| =3.5cm and |PR| = 8cm. Find |PQ|

Answer Details

We can use the property of similar triangles that corresponding sides are proportional. First, let's find the ratio of corresponding sides between the two triangles. Ratio of corresponding sides: |XY|/|PR| = 5/8 |XZ|/|PQ| = 3.5/|PQ| Since the two triangles are similar, the ratio of corresponding sides must be equal. Therefore: 5/8 = 3.5/|PQ| Cross-multiplying: 5 x |PQ| = 8 x 3.5 |PQ| = 28/5 Simplifying: |PQ| = 5.6 cm Therefore, |PQ| is 5.6 cm.