Answer:

Dimensions of rectangular box are:

l=12

b=x

h=9

The length of longest rod that can be placed in the box will be along central diagonal.

Length of central diagonal is

k= √l²+b²+h²

= 17= √12²+x²+9²

= 17= √144+x²+81

⇒289=225+x²

⇒x=√64 =8

So x=8

Verified answer

Step-by-step explanation:

[tex] \sf \large \: Given \: Dimensions :-[/tex]

● Length = 12

● Breadth = x

● Height = 9

To find X

[tex] \sf \: k = \sqrt{(l ^ 2 + b ^ 2 + h ^ 2)} \\ \sf \: \Rightarrow17= \sqrt {12^ 2 +x^ 2 +9^ 2} \\ \sf \Rightarrow17= \sqrt{ 144+x^ 2 +81 } \\ \sf \Rightarrow \: 289=225+x^ 2 \\ \sf \Rightarrow x= \sqrt{64} =8 \\ \sf \pink{ x = 8}[/tex]

Hope it'll help you ^_^