Question

If AABC is similar to ARST, find the value of x.

Answer 1

Given that

`\begin{gathered} \Delta ABC\text{ is similar to }\Delta RST \\ \text{Therefore, the ratio of the corresponding sides is equal.} \\ \text{That is,} \\ (AB)/(RS)=(BC)/(ST)=(AC)/(RT) \end{gathered}`

Given that AB = 12, BC =18, AC =24 and RS =16, RT=x

We now use the ratio of the corresponding sides to find side RT( the value of x).

Hence,

`\begin{gathered} (AB)/(RS)=(AC)/(RT) \\ (12)/(16)=(24)/(x) \\ x=(24*16)/(12) \\ x=32 \end{gathered}`

Therefore, the value of x (RT) is 32