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 ?
let the dimensions be a , b, and c cm
ab=600
ac=300
bc=200
from ab=600 , b =600/a
from ac=300 , c = 300/a
from bc = 200
(600/a)(300/a) = 200
180000/a^2 = 200
200a^2 = 180000
a^2 = 900
a = 30
then b=300/30 = 20
and c = 300/30 = 10
the cuboid is 30 cm by 20 cm by 10 cm
THANKS FOR THE ANSWER. :D
To find the sum of the length, breadth, and height of a cuboid, we need to determine the measurements of each dimension.
Let's assume the length of the cuboid is L, the breadth is B, and the height is H.
We are given that the areas of the three adjacent faces of the cuboid are 600 sq.cm, 300 sq.cm, and 200 sq.cm.
The area of a rectangle can be calculated by multiplying its length by its breadth. So, we have the following three equations:
L x B = 600 -- Equation 1
B x H = 300 -- Equation 2
L x H = 200 -- Equation 3
To solve these equations, we can use any method like substitution or elimination. Let's use the elimination method:
Multiplying Equation 1 by H: L x B x H = 600H -- Equation 4
Multiplying Equation 2 by L: B x H x L = 300L -- Equation 5
Multiplying Equation 3 by B: L x H x B = 200B -- Equation 6
From Equations 4, 5, and 6, we can see that L x B x H = 600H = 300L = 200B.
Dividing Equation 4 by H and Equation 5 by L, we get:
L x B = 600 -- Equation 7
B x H = 300 -- Equation 8
L x H = 200 -- Equation 9
Now, we can solve Equations 7, 8, and 9 to find the values of L, B, and H.
From Equation 7: L x B = 600, we can choose factors of 600 to find the values of L and B. The possible pairs are (1, 600), (2, 300), (3, 200), (4, 150), (5, 120), (6, 100), (8, 75), (10, 60), (12, 50), (15, 40), (20, 30), (24, 25).
From Equation 8: B x H = 300, we can check the pairs from the previous step to find the pair that gives the correct value of H. We see that when L = 6, B = 100, and H = 3 satisfy this equation.
Therefore, the cuboid has a length of 6 cm, a breadth of 100 cm, and a height of 3 cm.
Finally, the sum of the length, breadth, and height of the cuboid is: 6 + 100 + 3 = 109 cm.