The dimensions of a rectangular box are in the ratio 2:3:4. The difference between the cost of covering at the rate of 10Rs and 11Rs per m2 is 1300. Find the dimensions.
Answers
Answer:
Length = 10m, Breadth = 15m and Height = 20m
Step-by-step explanation:
Ratio = 2 : 3 : 4
Define x:
Let x be the constant ratio
Ratio = 2x : 3x : 4x
Find the surface area in term of x:
Total surface area = 2( lb + bh + lh)
Total surface area = 2( (2x)(3x) + (3x)(4x) + (4x)(2x) )
Total surface area = 2(6x² + 12x² + 8x²) = 52x²
If the cost is Rs 10 per m²
1 m² = Rs 10
52x² m² = 52x² x 10 = Rs 520x²
If the cost is Rs 11 per m²
1 m² = Rs 11
52x² = 52x² x 11 = Rs 572x²
Solve x:
The difference is Rs 1300
572x² - 520x² = 1300
52x² = 1300
x² = 1300 ÷ 52 = 25
x = √25
x = 5 m
Find the dimensions:
Length = 2x = 2(5) = 10 m
Breadth = 3x = 3(5) = 15 m
Height = 4x = 4(5) = 20 m
Answer: Length = 10m, Breadth = 15m and Height = 20m
Answer:
Length = 10m
Breadth = 15m
Height = 20m
Step-by-step explanation:
The given ratio of length, breadth and height is
L : B : H = 2 : 3 : 4
Now, suppose
Length = 2t
Then
Breadth = 3t
Height = 4t
Now our given ratio will become
Ratio = 2t : 3t : 4t
Lets find the surface area in term of x:
Total surface area = 2( LxB + BxH + LxH)
Total surface area = 2( (2t)(3t) + (3t)(4t) + (2t)(4t) )
Total surface area = 2(6t² + 12t² + 8t²)
Total surface area = 52t² m²
If we take the cost per square meter to be 10 RS, then our total cost becomes
(Total Cost)₁ = 10 x total surface area
(Total Cost)₁ = 10 x 52t²
(Total Cost)₁ = 520 t² m²
If we take the cost per square meter to be 11 RS, then our total cost becomes
(Total Cost)₂ = 11x total surface area
(Total Cost)₂ = 11 x 52t²
(Total Cost)₂ = 572 t² m²
Given that difference in covering cost at 11Rs and 10Rs is 1300.
So
(Total Cost)₂ -(Total Cost)₁ = 1300
572t² - 520t² = 1300
52t² = 1300
t² = 1300 ÷ 52 = 25
t = √25
t = 5 m
So our dimensions would be
Length = 2t = 2(5) = 10 m
Breadth = 3t = 3(5) = 15 m
Height = 4t = 4(5) = 20 m