why can you use an equation when solving for x in the diagram

Answer 1

In mathematics, equations are used to represent relationships between different variables. When solving for x in a diagram, we can often identify relevant variables and their relationships, and express them in the form of an equation.

For example, consider a diagram of a right triangle, where we know the lengths of two sides and want to find the length of the third side. By applying the Pythagorean theorem (which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides), we can write an equation involving the lengths of the sides. Solving this equation will give us the value of the unknown side length, satisfying the given diagram.

Equations allow us to mathematically represent the constraints and relationships present in a diagram, helping us to find unknown values or quantities. They provide a systematic approach to problem-solving, utilizing mathematical operations to simplify and solve for the desired variable.