Question

What is the maximum length of the pencil that can be kept in a rectangular box of dimensions 10cm × 12cm × 8cm ?​

Answer 1

$\LARGE{\underline{\purple{\sf{☘︎ Question}}}}$

What is the maximum length of the pencil that can be kept in a rectangular box of dimensions 10cm × 12cm × 8cm ?

$\LARGE{\underline{\purple{\sf{☘︎Answer}}}}$

The maximum length of the pencil is = $\fbox\orange{17 cm}$

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$\LARGE{\underline{\purple{\sf{☘︎ Explanation}}}}$

Given , Length = 10 cm

breadth = 12 cm

height. = 8 cm

.

Diagonal of cuboid = $\sqrt{ l²\:+\:b²\:+\:h²}$

$\Longrightarrow\:\:\sqrt{ (12)²\:+\:(9)²\:+\:(8)²}$

$\Longrightarrow\:\:\sqrt{144\:+\:81\:+\:64}$

$\Longrightarrow\:\:\sqrt{289}$

$\Longrightarrow\:\:\fbox\orange{17\:cm}$

.

.°. The Diagonal of the box = 17 cm

Hence, the maximum length of the pencil is = 17 cm

Answer 2

Explanation:

Given , Length = 10 cm

breadth = 12 cm

height. = 8 cm

$Diagonal of cuboid = \sqrt{ l²\:+\:b²\:+\:h²} l²+b²+h²$

$\Longrightarrow\:\:\sqrt{ (12)²\:+\:(9)²\:+\:(8)²}⟹ (12)²+(9)²+(8)²$

$\Longrightarrow\:\:\sqrt{144\:+\:81\:+\:64}⟹ 144+81+64$

$\Longrightarrow\:\:\sqrt{289}⟹ 289$

$\Longrightarrow\:\:\fbox\blue{17\:cm}⟹17cm$

.°. The Diagonal of the box = 17 cm

Hence, the maximum length of the pencil is = 17 cm