Question

o volume de um paralelepipedo retangulo 1620dmao cubo. calcular as dimensoes que sao proporcionais a 3,4 e 5dm

Answer 1

$Ola'~~~\mathbf{Mariele} \\ \\ Seja~os~lados~de~um~paralelepipedo ~retangular~\begin{cases}x \\ y \\ z\end{cases} \\ \\ Ent\~ao~o~volume~seria: \\\underbrace{ V}_{x.y.z}=1620dm\³~~~--\ \textgreater \ onde~[V=x.y.z] \\ \boxed{x.y.z=1620dm\³}~~---\ \textgreater \ (I) \\ \\ ==================================== \\ Nos~indica~que~as~dimes\~oes~s\~ao~proporcionais~oseja: \\ \frac{x}{3}= \frac{y}{4}= \frac{z}{5}~~--\ \textgreater \ igualemos~a~um~constante~(k), veja: \\ \\ \frac{x}{3}= \frac{y}{4} = \frac{z}{5}=k$

$\\ \\Igualando \begin{cases}x=3k \\ y=4k \\ z=5k\end{cases} \\ Agora~substituindo~em~(I)~temos: \\ \\ x.y.z=1620 \\ 3k.4k.5k=1620 \\ ~~~~60k\³ ~=1620 \\~~~~\boxed{k= 3}\\ \\ ==================================== \\ Agora~calculemos~cada~uma~das~dimes\~oes~veja: \\ x=3k \\ x=3( 3)=9dm \\ \\ y=4k \\ y=4( 3)=12dm \\ \\ z=5k \\ z=5( 3)= 15dm$

$As~dimes\~oes~s\~ao:~\boxed{\boxed{9dm~;~12dm~e~15dm}} \\ \\ \mathbb{ttttttttttttttttttttttttttttttttttttttt}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$