Mensuration Practice Test 9

l + b + h = 12
2(lb + bh + hl) = 94
Maximum length of the stick = $\sqrt{{\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^2}$
${\left(\mathit{l}+\mathit{b}+\mathit{h}\right)}^2$ = ${\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^2$ + 2 (lb + bh + hl)
${\left(12\right)}^2$ = ${\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^2$ (94)
144 - 94 = ${\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^2$
50 = ${\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^2$
$\sqrt{50}$ = $\sqrt{{\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^2}$
So, maximum length of the stick = $\sqrt{50}$
= $5\sqrt{2}$ cm