Answer to Question #94126 in Physics for Roaia

Question

If the volume of the cuboid =40cm^2 length = x+1 width =x high = 2
So x=

Answer 1

Given values: $V = 40\text{ cm}^3; l = x+1; w = x; h = 2\text{ cm}$ (units are assumed in order to assure the correct dimensions of respective values).

In order to simplify the script we will henceforth drop the notation of the units, having them implied, and operate with the numerical values only.

Equation for the volume:

$V = lwh = (x+1)\cdot x\cdot2 = 40; \\ x(x+1) = 20; \\ x^2 + x - 20 = 0.$

Now solving the quadratic equation for x,

$x_{1,2} = \frac{-1 \pm \sqrt{1 + 4\cdot1\cdot20} }{2\cdot1} = \frac{-1 \pm 9}{2} = -5 \text{ or } 4.$

Naturally the length/width by their nature and meaning would be positive values, so we select the positive result:

$x = 4\space [\text{cm}].$