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.
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