# Find the lenght of the diagonal of a rectangular shaped box whose edges are 3 cm , 4 cm and 12 cm .

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### 3 Answers

The formula for the diagonal is :

D= (length^2+width^+height^2)^1/2

D= (12^2*4^2*3^2)^1/2

= (144+16+9)^1/2= (169)^1/2= 13

The length of the diagonal is 13 cm

Te length of the digonal shaped box of edges are 3cm,4cm and 12cm:

Solution:

The diagonal is sqrt(3^2+4^2+12^2) = sqrt{9+16+144} = 13cm.

The diagonal of the botom face with 3 cm and 4cm is got by using the pytagorus theorem sqrt(3^2+4^2) = sqrt(25) =5cm.

Now the diagonal of the bottom face and the height 12cm of the opposite vertical edge make another right angled triangle whise diagonal is the diagon of the box which got by sqrt(5^2+12^2) = sqrt(169) = 13cm

The diagonal of a rectangular box has the formula :

D = ( l² + L² + h²)^1/2= (3² + 4² + 12²)^1/2= (9+16+144)^1/2 169^1/2= 13

Where

l= width= 3

L= length= 4

h= hight= 12