Initial area in cm³ = (3)(5)(8) = 120
New area = (x+3) (x+5) (8) = 8x² + 64x + 120
New area if 34 cm³ more than initial area. So if new area - 34 cm³ is equal to the initial area
8x² + 64x + 120 - 34 = 120
8x² + 64x + 86 = 120
8x² + 64x + 86 - 120 = 0
8x² + 64x -34 = 0
2 (4x² + 32x - 17) = 0
2 ( x - 1/2) (x + 17/2 ) = 0
x - 1/2 = 0 x + 17/2 = 0
x = 1/2 x = -17/2
Since increase means positive, so x = 1/2 is considered
So the new dimension of the enlarged rectangular metal is
(x + 3) (x + 5) (8)
(1/2 + 3) (1/2 + 5) (8)
3.5 cm by 5.5 cm by 8 cm
