Verified Answer :

  • Identify the expression as \(2(L + W)\) and given values \(L = 7\) and \(W = 3\).
  • Substitute the values to get \(2(7 + 3)\).
  • Perform the addition inside the parentheses: \(7 + 3 = 10\).
  • Multiply by \(2\) to reach the final value: \(2 \times 10 = \boxed{20}\).

Explanation

  1. Analysis of the expression and variables

To evaluate the expression \(2(L + W)\) with the given values \(L = 7\) and \(W = 3\), we first identify the expression and the variables provided. We are asked to compute the value of the perimeter-like formula where \(L\) represents length and \(W\) represents width. The objective is to substitute these specific numerical values into the algebraic expression and perform the required arithmetic operations.

  1. Evaluating the expression step by step

The first step in evaluating the expression is substitution. We replace the variables \(L\) and \(W\) with their assigned values of \(7\) and \(3\) respectively, resulting in the expression \(2(7 + 3)\). Next, we follow the order of operations by addressing the expression inside the parentheses first. Adding the numbers gives us \(7 + 3 = 10\). Finally, we multiply this sum by the coefficient \(2\), resulting in \(2 \times 10 = 20\).

Examples

This type of calculation is very common in geometry, for example, when finding the perimeter of a rectangle. If you have a rectangular garden plot with a length of \(7\) meters and a width of \(3\) meters, the total length of fencing required would be calculated as \(2 \times (7 \text{ m} + 3 \text{ m}) = 20 \text{ meters}\). Understanding how to evaluate such expressions is a foundational skill for calculating dimensions in real-world construction, design, and land management.

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