Question

The diagram below shows two similar isosceles triangles. What is the length of ST in triangle RST?A. 6cmB. 4cmC. 12cm D. 16cm

Answer 1

ST = 4cm

Step-by-step explanation

We want to find the length of ST in triangle RST.

We are given that the two triangles are similar.

In similar triangles, the ratio of proportional sides of the two triangles are equal for all sides.

This means that:

`(OP)/(RS)=(PQ)/(ST)=(OQ)/(RT)`

Therefore, to find the length of ST, we can apply the last two proportions. That is:

`\begin{gathered} (8)/(ST)=(4)/(2) \\ \Rightarrow ST=(8\cdot2)/(4) \\ ST=4\text{ cm} \end{gathered}`

That is the length of ST.