A rectangular parallelepiped has dimensions in arithmetic progression. If the sum of its dimensions is 21 cm and the volume is 168 cm³, find its dimensions.
Show answer & explanation
Correct answer: D
Explanation
Given:
Dimensions are in arithmetic progression.
Sum of dimensions = 21 cm
Volume = 168 cubic cm
By formula:
3a = 21
a = 7
Volume = (a − d) × a × (a + d)
Volume = (7 − d) × 7 × (7 + d)
168 = 7(49 − d²)
168 = 343 − 7d²
7d² = 343 − 168
7d² = 175
d² = 25
d = 5
If dimensions are a − d, a, a + d
7 − 5 = 2 cm
7 = 7 cm
7 + 5 = 12 cm
Dimensions = 2 cm, 7 cm, 12 cm