PLZ HELP 4 The three different face diagonals of a cuboid ( rectangular parallclopiped ) - Maths - Introduction to Three Dimensional Geometry

Question

PLZ HELP
4 The three different face diagonals of a cuboid ( rectangular
parallclopiped ) have lengths 39, 40, 41 The length of the main
diagonal of the cuboid which joins a pair of opposite corners
is
A 49
B 49 2
C 60
D 60 2

Manisha Sachdeva · Accepted Answer

Dear student,

Let l, b and h be the length, breadth and height of the cuboid

Given that the three face diagonals are 39, 40, 41

l2+b2=392     1b2+h2=402   
2l2+h2=412   
3Adding 1, 2 and 3, we get2l2 + b2 + h2 = 392 + 402 + 412 = 1521+1600+1681 = 4802⇒l2 + b2 + h2 = 2401⇒l2 + b2 + h2 = 49So, length of main diagonal of cuboid = 49 m

Regards

PLZ HELP.... 4. The three different face diagonals of a cuboid ( rectangular parallclopiped ) have lengths 39, 40, 41. The length of the main diagonal of the cuboid which joins a pair of opposite corners is A. 49 B. 49 2 C. 60 D. 60 2

PLZ HELP....
4. The three different face diagonals of a cuboid ( rectangular parallclopiped ) have lengths 39, 40, 41. The length of the main diagonal of the cuboid which joins a pair of opposite corners is
A. 49
B. 49 $\sqrt{2}$
C. 60
D. 60 $\sqrt{2}$