Problem 11 - Introductory Algebra for College Students

Question

A rectangle has a width of 44 centimeters and a perimeter of 188 centimeters. What is the rectangle's length?

Step-by-Step Solution

Answer

The length of the rectangle is 50cm.

Step 1: Understanding the problem

We are given that the width of the rectangle is 44cm and the perimeter is 188cm. The problem is asking for the length of the rectangle. We can use the formula of the perimeter of a rectangle, which is Perimeter = 2*(Length + Width), to solve for the length.

Step 2: Rearranging the formula

We can rearrange the formula for the rectangle's perimeter to isolate the length on one side. This gives us Length= (Perimeter/2) - Width.

Step 3: Substitute the given values into formula

Now, substitute the given values into the rearranged formula. So, Length= (188cm/2) - 44cm.

Step 4: Calculate length

After substituting the given values, it gives Length=94cm - 44cm. Thus, the length of the rectangle is 50cm. Hence validate the answer now by substituting length and width in the formula of Perimeter, which must equal to the given perimeter i.e., 188cm.

Step 5: Validation

By substituting Length=50cm, Width=44cm in the Perimeter = 2*(Length + Width) formula, the Perimeter is indeed 188cm, which validates the answer.