# The dimension of rectangular metal box are 3cm 5cm and 8 cm. if the first 2 dimension are increased by the same numbrs of centimeters, while the 3rd dimension remains the same, the new volume is 34cmcube more than the original volume. what is the new dimension of the enlarged rectangular metal box? Need a solution Thank you

1
by xAchillesx

2015-08-20T20:50:03+08:00

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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