The length, breadth and height of a cuboid are in the ratio of 6: 4:3. If the total surface area of the cuboid is 972 cm², what is the length (in cm) of the diagonal of the cuboid?
Let the length (l), breadth (b), and height (h) of the cuboid can be l = 6x, b = 4x, h = 3x
TSA = 2(lb + bh + hl)
972 = 2((6x)(4x) + (4x)(3x) + (3x)(6x))
972 = 2(24x² + 12x² + 18x²)
972 = 108x²
x² = 9
x = 3
Length (l) = 6x = 6 ×3 = 18 cm
Breadth (b) = 4x = 4 ×3 = 12 cm
Height (h) = 3x = 3 ×3 = 9 cm
d = √(l² + b² + h²)
d = √(18² + 12² + 9²)
d = √(324 + 144 + 81)
d = √549
d = 3√61 cm
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