Question
Download Solution PDFThe length, width and height of a cuboid are in the ratio 10 : 17 : 14, and its total surface area is 1096 cm2. Find the length (in cm) of the cuboid.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The length, width, and height of a cuboid are in the ratio 10:17:14.
Total surface area = 1096 cm2
Formula used:
Total surface area of a cuboid = 2 × (length × width + width × height + height × length)
Let the length = 10x, width = 17x, and height = 14x.
Calculation:
Total surface area = 2 × (length × width + width × height + height × length)
1096 = 2 × [(10x × 17x) + (17x × 14x) + (14x × 10x)]
⇒ 1096 = 2 × [170x2 + 238x2 + 140x2]
⇒ 1096 = 2 × 548x2
⇒ 1096 = 1096x2
⇒ x2 = 1
⇒ x = 1
Length = 10x = 10 × 1 = 10 cm
∴ The correct answer is option (3).
Last updated on Jul 17, 2025
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