-
The ratio of the length and breadth of a rectangular parallelopiped is 5 : 3 and its height is 6 cm. If the total surface area of the parallelopiped be 558 sq. cm, then its length in dm is
-
- 9
- 1.5
- 10
- 15
- 9
Correct Option: B
Length = 5x cm Breadth = 3x cm
Total surface area of parallelopiped = 2(l × b + b × h + h × l)
= 2(5x × 3x + 3x × 6 + 6 × 5x)
= 2(15x² + 18x + 30x)
= 2 (15x² + 48x)
∴ 2(15x² + 48x) = 558
| ⇒ 15x² + 48x = | = 279 | |
| 2 |
⇒ 5x² + 16x = 93
⇒ 5x² + 16x – 93 = 0
⇒ 5x² + 31x – 15x – 93 = 0
⇒ x (5x + 31) – 3 (5x + 31) = 0
⇒ (x – 3) (5x + 31) = 0
⇒ x = 3
∴ Length = 5x = 5 × 3 = 15 cm
= 1.5 dm
