The length and breadth of a cuboid are in the ratio 4:5.The height and total surface area of the cuboid are 18 cm and 3384 cm^2 respectively. Find its length and breadth
Answers
Length of the cuboid = 24 cm and breadth of the cuboid = 30 cm.
Given:
The length and breadth of a cuboid are in the ratio of 4:5
The cuboid's height and total surface area are 18 cm and 3384 cm² respectively.
To find:
Find its length and breadth
Solution:
Formula used:
Total surface area of the cuboid = 2 (lb + bh + lh) square units
Let l and b be the length and breadth of the cuboid
From the given data, l: b = 4: 5
=> l/b = 4/5
=> l = 4b/5 --- (1)
By the given formula,
The total surface area of the cuboid
= 2 [ 4b/5(b) + bh + (4b)h/5)
= 2 [ (4b²)/5 + bh + (4bh)/5)
Given that height = 18 cm
= 2 [ (4b²)/5 + 18b + (72b)/5 ]
= 2 [ 4b² + 90b + 72b ]/5
Given that the total surface area of the cuboid = 3384 cm²
=> 2 [ 4b² + 90b + 72b ]/5 = 3384
=> 2 [ 4b² + 90b + 72b ] = 16920
=> [ 4b² + 90b + 72b ] = 4230
=> 2b² +81b - 4230 = 0
=> 2b² + 60b - 141b - 4230 = 0
=> 2b(b + 30b) - 141(b + 30b) = 0
=> (b - 30) (2b + 141) = 0
=> b - 30 = 0 or 2b + 141 = 0
=> b = 30 2b = - 141 [ which is not possible ]
Thus, the breadth of the cuboid = 30 cm
=> Length of the cuboid, l = 4(30)/5 = 24 cm
Therefore,
Length of the cuboid = 24 cm and breadth of the cuboid = 30 cm.
#SPJ3