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.
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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
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