Establishing an Equation

We will discuss here about establishing an equation.

In a given context, the relation between variables expressed by equality (or inequality) is called a formula. When a formula is expressed by an equality, the algebraic expression is called an equation.

Step I: Symbolize the variables of the context by a, x, A, X, etc.

Step II: Use the laws or conditions of the context to establish equality (or inequality) between the variables.

This equality (or inequality) between the variables is a formula for the variables . In case of equality, we get an equation.

Solved examples on establishing an equation or framing a formula:

1. Let the base of a triangle be b, its height h and the area A.

The context is form mensuration. We know that

area of a triangle = \(\frac{1}{2}\) × base × height.

Therefore, A = \(\frac{1}{2}\) bh. This is the formula for the given context.

It generates a simple rule of mensuration for finding the area of a triangle.

2. Let a sum of $ P be invested in a bank at a simple interest rate of r% per annum for a period of n years. At the end of n years an amount of $ A is obtained. 

The context is form arithmetic. We know that

Amount = Principal + Interest.

We know that

Interest = \(\frac{\textbf{Principal × Rate × Time}}{100}\)

Therefore, A = P + \(\frac{\mathrm{P \times r \times n}}{100}\)

This is the formula for the given context.

9th Grade Math

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