Question

Triangles PQR and XYZ are similar. What is the length of XZ? 6 5.25 3.5 2.57

Answer 1

Option B: 5.25 is the length of XZ

Step-by-step explanation:

The triangles PQR and XYZ are similar.

To determine the length of XZ, let us use the similarity theorem.

The theorem states that, "if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar".

Thus,

`(QR)/(YZ) =(PR)/(XZ)`

Let us substitute the values from the diagram, we have,

`(4)/(3) =(7)/(XZ)`

Multiplying both sides by 3, we get,

`4 =(21)/(XZ)`

Thus,

`XZ =(21)/(4)=5.25`

Thus, the length of XZ is 5.25

Hence, Option B is the correct answer.