Answer:
TU = 21.6
Step-by-step explanation:
If two triangles are similar, their corresponding sides are always in the same ratio.
Given that ΔPQR ~ ΔSTU then:
[tex]\dfrac{PQ}{ST}=\dfrac{QR}{TU}[/tex]
Plug in the given side lengths PQ = 4, QR = 2.7, and ST = 32:
[tex]\dfrac{4}{32}=\dfrac{2.7}{TU}[/tex]
Cross multiply:
[tex]4\cdot TU=2.7 \times 32[/tex]
Now, solve for TU:
[tex]TU=\dfrac{2.7 \times 32}{4}\\\\\\TU=\dfrac{86.4}{4}\\\\\\TU=21.6[/tex]
Therefore, the length of side TU is:
[tex]\Large\boxed{\boxed{TU=21.6}}[/tex]
