# The volume of a rectangular box is #270# #m^3#. The width of the box is 3 meters less than the length. The height is 5 meters. What is the length of the box?

Length of the rectangular box is

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Let's denote the length of the box as ( L ). Given that the width is 3 meters less than the length, the width will be ( L - 3 ). The height is given as 5 meters.

The formula for the volume of a rectangular box is ( \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} ).

Substituting the given values into the formula, we get:

[ 270 = L \times (L - 3) \times 5 ]

Now, let's solve for ( L ):

[ 270 = 5L(L - 3) ]

[ 270 = 5L^2 - 15L ]

[ 5L^2 - 15L - 270 = 0 ]

Now, we have a quadratic equation. We can solve this equation using the quadratic formula:

[ L = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

Where ( a = 5 ), ( b = -15 ), and ( c = -270 ).

[ L = \frac{-(-15) \pm \sqrt{(-15)^2 - 4 \times 5 \times (-270)}}{2 \times 5} ]

[ L = \frac{15 \pm \sqrt{225 + 5400}}{10} ]

[ L = \frac{15 \pm \sqrt{5625}}{10} ]

[ L = \frac{15 \pm 75}{10} ]

This gives us two potential values for ( L ):

- ( L = \frac{15 + 75}{10} = \frac{90}{10} = 9 )
- ( L =

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