Answer:
see explanation
Step-by-step explanation:
The volume (V) of a cuboid is calculated using the formula
V = lbh ( l is length, b is breadth and h is height )
Equate the product of the dimensions to 374
2(x + 3)(x + 9) = 374 ( divide both sides by 2 )
(x + 3)(x + 9) = 187 ← expand factors on left side
x² + 12x + 27 = 187 ( subtract 187 from both sides )
x² + 12x - 160 = 0 ← in standard form
Factor by considering the factors of the constant term (- 160) which sum to give the coefficient of the x- term (+ 12)
The factors are + 20 and - 8, hence
(x + 20)(x - 8) = 0
Equate each factor to zero and solve for x
x + 20 = 0 ⇒ x = - 20
x - 8 = 0 ⇒ x = 8
solutions are x = - 20, x = 8
However x > 0 ⇒ x = 8 and
x + 3 = 8 + 3 = 11
x + 9 = 8 + 9 = 17
Dimensions are 2cm, 11 cm, 17 cm
