Question

The ratio of length ,breadth and height of cuboid is 6 : 5 : 4 .Find the length of cuboid if total surface area is 1332 sq.cm
(1) 12 cm (2) 15cm (3) 18 cm (4) 20 cm

Answer 1

Solution

Given :-

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

Find :-

• Length of cuboid .

Explanation

Let,

• Length be(L) = 6x
• Breadth be(B) = 5x
• Height be(H) = 4x

Using Formula

$\boxed{\underline{\tt{\red{\:Cuboid_{TSA}\:=\:2(LB+BH+HL)}}}}$

Keep all values,

➡ Total Surface area of cuboid = 2(6x × 5x + 5x × 4x + 4x × 6x)

➡ 1332 = 2(30x² + 20x² + 24x²)

➡1332/2 = 74x²

➡x² = 666/74

➡x² = 9

➡x = ±√9

➡x = ±3

We know,

Length be always positive ,

So, neglect x = -3,

Since, take

• x = 3

Hence

• Length will be (L) = 6x = 6 × 3 = 18
• Breadth will be (B) = 5x = 5 × 3 = 15
• Height will be (H) = 4x = 4 × 3 = 12

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Answer 2

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Solution

Given :

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

Find :

• Length of cuboid .

Explanation

Let,

• Length be(L) = 6x
• Breadth be(B) = 5x
• Height be(H) = 4x

Using Formula

$\boxed{\underline{\tt{\pink{\:Cuboid_{TSA}\:=\:2(LB+BH+HL)}}}}$

Keep all values,

➡ Total Surface area of cuboid = 2(6x × 5x + 5x × 4x + 4x × 6x)

➡ 1332 = 2(30x² + 20x² + 24x²)

➡1332/2 = 74x²

➡x² = 666/74

➡x² = 9

➡x = ±√9

➡x = ±3

We know,

• Length be always positive ,

• So, neglect x = -3,

• Since, take

• x = 3

Hence

• Length will be (L) = 6x = 6 × 3 = 18
• Breadth will be (B) = 5x = 5 × 3 = 15
• Height will be (H) = 4x = 4 × 3 = 12

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$@\green{\underline{\boxed{\sf ʙʀᴀɪɴʟʏ :}}}$

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