Question

The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm², find the length, breadth and height of the solid. Also find the length of a diagonal of the cuboid.

Answer 1

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Answer 2

L = 80 cm; B = 64 cm; H = 32 cm. Diagonal = 83.81 cm

Explanation:

Let the sides of the cuboid be 5x, 4x and 2x for length, breadth and height respectively.

Total surface area = 1216 cm²

2 (lb + bh + lh) = 1216

Substituting the values, we get:

2 (5x*4x + 4x*2x + 2x*5x) = 1216

20x + 8x + 10x = 608

38x = 608

Therefore x = 608 / 38 = 16.

So length = 5x = 5 * 16 = 80 cm.

Breadth = 4x = 4 * 16 = 64 cm.

Height = 2x = 2 * 16 = 32 cm.

To find the diagonal, we use the pythagoras theorem.

Hypotenuse = root of sum of square of two sides of the right angled triangle

Diagonal = root of (length^2 + height^2)

= root of (80*80 + 32*32)

= root of 7424

Length of the diagonal = 83.81 cm