Graduate Management Admission Test (GMAT) Practice Test

How can you determine the dimensions of a rectangle given its area and perimeter?

1. Find the rectangle's factors and add

2. Determine area's factors and check their sum

3. Multiply the area by the perimeter

4. Use the area to divide the perimeter

The correct answer is: Determine area's factors and check their sum

To determine the dimensions of a rectangle using its area and perimeter, it is essential to understand the relationship between these two properties and how they can help derive the length and width of the rectangle. The area of a rectangle is given by the formula \(A = l \times w\), where \(l\) is the length and \(w\) is the width. The perimeter is calculated using the formula \(P = 2(l + w)\). Given both area and perimeter, you can set up these two equations. Option B is correct because it suggests determining the factors of the area and then checking their sum to see if they correspond to the perimeter. By listing out the pairs of factors of the area, you can calculate potential length and width combinations. Then, by checking the sum of each combination, you can verify which set of dimensions meets the condition set by the perimeter. For example, if the area is 12, the factor pairs are (1,12), (2,6), and (3,4). For each pair, you would check if \(2(l + w)\) equals the given perimeter. This method is systematic and directly relates the two dimensions through the relationships provided in the formulas for area and perimeter,