Question

The areas of the the three adjacent faces of a cuboid are 600 sq.cm 300sq.cm and 200 sq.cm.find the sum of the length,breadth and height of the cuboid ?

Answer 1

Solution:-
Let the Length, Breadth and Height of the cuboid be 'x' cm, 'y' cm and 'z cm respectively.
Therefore,
x × y = 600 sq. cm
⇒ xy = 600
⇒ y = 600/x ........(1)
x × z = 300 sq. cm
⇒ xz = 300
⇒ z = 300/x .........(2)
yz = 200 sq. cm .....(3)
Putting the value of y = 600/x and z = 300/x in the equation (3) i.e. yz =200, we get
⇒ (600/x) × (300/x) = 200 
⇒ 180000/x² = 200
⇒ x² = 180000/200
⇒ x² = 900
⇒ x = √900
x = 30 
So the Length is 30 cm.
Putting the value of x = 30 in equation (1), we get
y = 600/x
y = 600/30
⇒ y = 20 cm
Putting the value of y = 20 cm in the equation (3), we get
yz = 200
⇒ 20 × z = 200
⇒ z = 200/20
z =10
Length = 30 cm, Breadth = 20 cm and Height = 10 cm
Answer