Question

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

Answer 1

Given that

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

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,

$\begin{gathered} \frac{AB}{RS}=\frac{AC}{RT} \\ \frac{12}{16}=\frac{24}{x} \\ x=\frac{24\times16}{12} \\ x=32 \end{gathered}$

Therefore, the value of x (RT) is 32