Question

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

Answer 1

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

Answer 2

Step-by-step explanation:

$\sf \large \: Given \: Dimensions :-$

● Length = 12

● Breadth = x

● Height = 9

To find X

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

Hope it'll help you ^_^