Question

The ratio of length,breadth and height of cuboid is 6:5:4. Find the length of the cuboid if total surface area is 1332 sq.cm​

Answer 1

`\huge \bold \: \bf \: Solution`

Let ,

• Length = 6x
• Breadth = 5x
• Height = 4x

`\sf \: Formula`

• TSA = 2( LB + BH + HL )

`\displaystyle \large \sf \mapsto \: 2(lb \: + \: bh \: + hl) = 1332`

`\displaystyle \large \sf \mapsto \: 2(6x * 5x + 5x * 4x + 4x * 6x )= 1332`

`\displaystyle \large \sf \mapsto2(30 {x}^(2) + {20x}^(2) + {24x}^(2) ) = 1332`

`\displaystyle \large \sf \mapsto \: 2(74 {x}^(2) ) = 1332`

`\displaystyle \large \sf \mapsto148 {x}^(2) = 1332`

`\displaystyle \large \sf \mapsto \: x {}^(2) = 9`

x = √9

x = 3

Now,

Putting the value of

Length

• 6x = 6×3 = 18

Breadth

• 5x = 5×3 = 15

Height

• 4x = 4×3 =12

Thus, Length of cuboid = 18 cm.

Answer 2

• Length of the cuboid is 18 cm.

Explanation:

Given,

• The ratio of length,breadth and height of cuboid is 6:5:4.
• Total surface area = 1332 cm²

Let's assume,

• Length of cuboid = 6x
• Breadth of cuboid = 5x
• Height of cuboid = 4x

We know that,

• TSA of cuboid = 2(lb + bh + hl)

On substituting the values we get,

→ 2(6x × 5x) + (5x × 4x) + (4x × 6x) = 1332

→ 2 ( 30x² + 20x2 + 24x²) = 1332

→ 2 × 74x² = 1332

→ 74x² = 1332/2

→ 74x² = 666

→ x² = 666/74

→ x² = 9

→ x = √9

→ x = 3

Hence,

Length of cuboid :

→ 6x

→ 6 × 3

→ 18 cm

Therefore, length of the cuboid is 18 cm.