KnowledgeBoat Logo
|

Mathematics

The internal dimensions of a rectangular box are 12 cm ×\times x cm ×\times 9 cm. If the length of the longest rod that can be placed in this box is 17cm; find x.

Mensuration

6 Likes

Answer

Given:

Dimensions of the box = 12 cm ×\times x cm ×\times 9 cm

Length of longest diagonal = l2+b2+h2\sqrt{l^2 + b^2 + h^2}

⇒122+x2+92=17⇒[122+x2+92]2=(17)2⇒122+x2+92=289⇒144+x2+81=289⇒225+x2=289⇒x2=289−225⇒x2=64⇒x=64⇒x=8⇒ \sqrt{12^2 + x^2 + 9^2} = 17\\[1em] ⇒ \Big[\sqrt{12^2 + x^2 + 9^2}\Big]^2 = (17)^2\\[1em] ⇒ 12^2 + x^2 + 9^2 = 289\\[1em] ⇒ 144 + x^2 + 81 = 289\\[1em] ⇒ 225 + x^2 = 289\\[1em] ⇒ x^2 = 289 - 225\\[1em] ⇒ x^2 = 64\\[1em] ⇒ x = \sqrt{64}\\[1em] ⇒ x = 8

Hence, the value of x is 8 cm.

Answered By

4 Likes

Related Questions