Question

The maximum length of a pencil that can be kept in a rectangular box of dimensions $12cm\times 9cm\times 8cm$, is

(a) $13cm$

(b) $17cm$

(c) $18cm$

(d) $19cm$

Answer 1

The correct option is (b): $17cm$

Length $\left(l\right)=12cm$

Breadth $\left(b\right)=9cm$

height $\left(h\right)=8cm$

$\therefore$ Maximum length of diagonal (pencil) = Diagonal of the rectangular box (Cuboidal in shape)

$=\sqrt{l^2+b^2+h^2}$

$=\sqrt{(12{)}^2+(9{)}^2+(8{)}^2}$

$=\sqrt{144+81+64}$

$=\sqrt{289}=17cm$