Question

In the sketch below, A ABC is similar to AXY Z. Find the length of side x

Answer 1

Step-by-step explanation

From geometry, we know that if two triangles are similar, then their corresponding sides are in proportion.

From the statement, we know that ΔABC is similar to ΔXYZ.

From the diagram, we see that:

• AB = 15 is the corresponding side to XY = 10,

,

• BC = 9 is the corresponding side to YZ = x.

So we must have the equality:

`\begin{gathered} (AB)/(XY)=(BC)/(YZ), \\ (15)/(10)=(9)/(x), \\ 1.5=(9)/(x). \end{gathered}`

Solving for x, we get:

`\begin{gathered} 1.5x=9, \\ x=(9)/(1.5)=6. \end{gathered}`Answer

x = 6