Multiple choice

The length, breadth and height of a rectangular solid are in the ratio $5 : 4 : 2$. If the total surface area is $1216$ cm$^{2}$, find the length, breath and height of the solid.

  1. $20$ cm, $16$ cm, $8$ cm
  2. $14$ cm, $12$ cm, $8$ cm
  3. $11$ cm, $19$ cm, $8$ cm
  4. $21$ cm, $11$ cm, $8$ cm
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A Correct answer
Explanation

Let dimensions be 5x, 4x, 2x. Surface Area = 2(lw + lh + wh) = 2(20x^2 + 10x^2 + 8x^2) = 2(38x^2) = 76x^2. 76x^2 = 1216 => x^2 = 16 => x = 4. Dimensions are 20, 16, 8.

AI explanation

The total surface area of a cuboid is calculated as twice the sum of the products of its length and breadth, breadth and height, and height and length. Let the dimensions be 5x, 4x, and 2x, which gives the equation 1216 equals 2 times the sum of 20x squared, 8x squared, and 10x squared. Solving 76x squared equals 1216 yields x equals 4. Multiplying the ratio values by 4 gives the dimensions as 20 cm, 16 cm, and 8 cm.

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