Quadratic function and equation in one variable

Question

A cuboid.

Height = (2x-5) cm

Width = 4 cm

Length = (x+3) cm

Given that the volume of the cuboid is 252 cm³. Find the total surface area, in cm², of the cuboid.

Answer 1

V = hwl

=> 252 = (2x - 5)(4)(x+3) = 4(2x² - 5x + 6x - 15) = 8x² + 4x - 60

=> 8x² + 4x - 60 - 252 = 0

=> 8x² + 4x - 312 = 0

=> 4(2x² + x - 78) = 0

=> 4(2x + 13)(x - 6) = 0

=> 2x + 13 = 0 => 2x = -13 => x = -6.5 (not possible for cuboid)

=> x - 6 = 0 => x = 6

hence h = 7, w = 4, l = 9 (check: 4 x 7 x 9 = 4 x 63 = 252)

surface = 2(hw) + 2(hl) + 2(wl) = 2(7.4) + 2(7.9) + 2(4.9) = 56 + 126 + 72 = 254 cm²