The competition swimming pool at Saanich Commonwealth Place...

The competition swimming pool at Saanich Commonwealth Place is in the shape of a rectangular prism and has a volume of $2100 \mathrm{m}^{3} .$ The dimensions of the pool are $x$ metres deep by $25 x$ metres long by $10 x+1$ metres wide. What are the actual dimensions of the pool?

Key Concepts

Polynomial Equations

Polynomial equations are mathematical expressions that involve sums and products of variables raised to various powers. In problems involving volume, setting up the equation often leads to a polynomial equation where one must solve for the unknown dimension. Mastering polynomial equations is pivotal in algebra, enabling the translation of geometric conditions into solvable mathematical problems.

Factoring and Solving Equations

Factoring is a method of decomposing a polynomial into a product of simpler expressions, which makes solving the equation more manageable. This skill is crucial in algebra for finding the values of unknown variables, particularly in practical scenarios where the dimensions or other characteristics of a figure must satisfy given conditions, such as a fixed volume.

Rectangular Prism

A rectangular prism is a three-dimensional geometric figure with six rectangular faces. The volume of a rectangular prism is calculated by multiplying its three dimensions (length, width, and height). This concept is fundamental in geometry and is frequently applied to problems in construction, design, and real-world applications involving space and volume.

Volume Calculation

Volume calculation is the process of determining the amount of space an object occupies. In the case of a rectangular prism, the volume is found by multiplying its three dimensions. This principle not only applies to simple geometric shapes but also underpins more complex applications in physics, engineering, and various fields where spatial analysis is required.

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