Question

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The dimensions of a rectangular box are in the ratio of 2: 3: 4 and the difference between the cost of covering it with sheet of paper at the rates of Rs 8 and Rs 9.50 per m2 is Rs 1248. Find the dimensions of the box.


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Answer 1

Answer:

Given :-

• The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rate of Rs 8 and Rs 9.50 per m² is 1248.

To Find :-

• What is the dimensions of the box.

Solution :-

Let,

➲ Length = 2x

➲ Breadth = 3x

➲ Height = 4x

As we know that :-

➜ Total Surface Area or TSA of Rectangular Box :

✫ TSA of Rectangular Box = 2(LB + BH + HL)

where,

• L = Length
• B = Breadth
• H = Height

According to the question by using the formula we get,

⇒ Total Surface Area = 2{(2x × 3x) + (3x × 4x) + (4x × 2x)

⇒ Total Surface Area = 2(6x² + 12x² + 8x²)

⇒ Total Surface Area = 2(18x² + 8x²)

⇒ Total Surface Area = 2(26x²)

⇒ Total Surface Area = 2 × 26x²

➡ Total Surface Area = 52x² m²

According to the question,

↦ {9.50(52x²) - 8(52x²)} = 1248

↦ (494x² - 416x²) = 1248

↦ 78x² = 1248

↦ x² = 1248/78

↦ x² = 16

↦ x = √16

↦ x = √4 × 4

➠ x = 4

Hence, the required dimensions are :

➣ Length of a rectangular box :

➞ Length = 2x

➞ Length = 2 × 4

➦ Length = 8 cm

➣ Breadth of a rectangular box :

➞ Breadth = 3x

➞ Breadth = 3 × 4

➦ Breadth = 12 cm

➣ Height of a rectangular box :

➞ Height = 4x

➞ Height = 4 × 4

➦ Height = 16 cm

∴ The dimensions of a rectangular box are 8 cm, 12 cm and 16 cm respectively.

Answer 2

Answer:

• The Length = 8m
• The Breadth = 12m
• The Height = 16m

Step-by-step explanation:

Given,

• The dimensions of a rectangular box are in the ratio of 2 : 3 : 4.
• The difference between the cost of covering it with sheet of paper at the rates of Rs 8 and Rs 9.50 per m² is Rs 1248.

To Find,

• The dimensions of the box.

Solution,

It's A Rectangular Box.

• We Can Say It CUBOID.

Let's,

• The Length = 2x
• The Breadth = 3x
• The Height = 4x

TSA of Cuboid = 2(LB + BH + HL)

→ TSA of Cuboid = 2 [2x(3x) + 3x(4x) + 4x(2x)]

→ TSA of Cuboid = 2 [6x² + 12x² + 8x²)

→ TSA of Cuboid = 2 [26x²]

→ TSA of Cuboid = 52x²m²

According To Question,

→ 9.5(52x²) - 8(52x²) = 1248

→ 494x² - 416x² = 1248

→ 78x² = 1248

→ x² = 16

→ x = 4m

The Length = 2x

• The Length = 8m

The Breadth = 3x

• The Breadth = 12m

The Height = 4x

• The Height = 16m

Required Answer,

• The Length = 8m
• The Breadth = 12m
• The Height = 16m