Question

The surface area of the cuboid is 1372 sq.cm if its dimensions are in the ratio of 4:2:1 then find ius length

Answer 1

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Answer 2

AnsweR:

Let the dimensions of cuboid be

• 4x
• 2x and,
• 1 x

Total surface area of cuboid = 2(lb+bh+hl)

$\hookrightarrow \tt \: 1372 = 2(4x \times 2x + 2x \times 1x + 1x \times 4x) \\ \\ \tt \hookrightarrow \: 1372 = 2(8x + 2x + 4x) \\ \\ \tt \hookrightarrow1372 = 2(14x) {}^{2} \\ \\ \hookrightarrow \tt 1372 = 28 {x}^{2} \\ \\ \hookrightarrow \tt {x}^{2} = \cancel \frac{1372}{28} = 49 \\ \\ \hookrightarrow \tt \: x = \sqrt{49} \\ \\ \hookrightarrow \tt \: x = 7 \: cm$

• Length = 4x = 4 × 7 = 28 cm
• Breadth = 2x = 2 × 7 = 14 cm
• Height = 1x = 1 × 7 = 7 cm.

Therefore, Length of the cuboid will be 28 cm.