Question

Dimensiunile unui paralelipiped dreptunghic sunt direct proporționale cu numerele 6;8;24 iar diagonala are lungimea 13 cm. Aflati volumul paralelipipedului.Dai coroana este urgent!

Answer 1

$l;h;L \ \ \ d.p. \\ 6;8;24 \\\\ \Longrightarrow \frac{l}{6}=\frac{h}{8}=\frac{L}{24}=k \\\\ l=6k \\ h=8k \\ L=24k \\\\\\ d=\sqrt{l^2+L^2+h^2} \\\\ 13=\sqrt{(6k)^2+(8k)^2+(24k)^2} \ \ \ |^2\\\\ 13^2=36k^2+64k^2+576k^2 \\\\ 169=676k^2 \\\\ k^2= \frac{\not 169}{\not 676} \\\\ k^2=\frac{1}{4} \\\\ \underline{k=\frac{1}{2}} \\\\\\ l=6*\frac{1}{2} \to3 \\ h=8*\frac{1}{2}\to 4 \\L=24*\frac{1}{2} \to 12 \\\\\\ V=L*l*h \\\\ V=3*4*12 \\\\\\ \boxed{V=144 \ cm^3}$