Formulas

A formula is an equation that describes a relationship between unknown values. Many problems are solved easily if the correct formula is known. To use formulas to solve problems, perform the following steps:

  1. Identify the appropriate formula.

  2. Replace the variables in the formula with their known values.

  3. Solve the formula for the remaining variable(s).

  4. Check the solution in the original problem.

  5. State the solution.

Example 1

Find the length of a rectangle (see Figure 1) if its perimeter is 48 inches and its width is 8 inches.

An appropriate formula is p = 2 l + 2 w, where p represents the perimeter, l the length, and w the width of the rectangle. Replace each variable with its known value.

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Now, solve for the remaining variable.

48 = 2 l + 16

Add –16 to both sides.

32 = 2 l

Multiply each side by equation (or divide each side by 2).

16 = l

Check with the original problem.

equation

The length of the rectangle is 16 inches.

Figure 1. Perimeter of a rectangle.

figure

Example 2

As shown in Figure 2, an area rug is in the shape of a trapezoid. Its area is 38 square feet, its height is 4 feet, and one of its bases is 7 feet long. Find the length of the other base.

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The check is left to you. The other base has a length of 12 feet.

Many times, a formula needs to be solved for one of its variables in terms of the other variables. To do this, simply perform the steps for solving equations as before but, this time, isolate the specified variable.

Figure 2. Area of trapezoid.

figure

Example 3

RT = D ( Rate × Time = Distance). Solve for R.

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Example 4

A = P + PRT ( Accumulated interest = Principal + Principal × Rate × Time). Solve for T.

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