A cuboid has a breadth of 5 cm, and the combined total of its length and height is 23 cm. If the volume of the cuboid is 600 cm³, calculate the percentage by which the length exceeds the height. (Note: The length of the cuboid is greater than its height.)
Let the length of the cuboid be ‘x’ cm Therefore, height of the cuboid = (23 – x) cm According to the question, 5 × x(23 – x) = 600 Or, x(23 – x) = 120 Or, x2 – 23x + 120 = 0 Or, x2 – 15x – 8x + 120 = 0 Or, x(x – 15) – 8(x – 15) = 0 Or, (x – 15)(x – 8) = 0 Or, x = 15, 8 Length of the cuboid = 15 cm then height of the cuboid = 23 – 15 = 8 cm Required percentage = (15 – 8)/8 × 100 = 87.5% Hence, option e.
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