Question

Rectangle R has length 30 and width 10, and square S has length 5. The perimeter of S is what fraction of the perimeter of R?

Hint:

Always ensure you simplify fractions to their lowest terms unless the question specifies otherwise. In this case, \(\frac{20}{80}\) simplifies to \(\frac{1}{4}\).

Answer 1

Step 1: Understanding the Concept:
This problem requires calculating the perimeters of a rectangle and a square and then expressing the ratio of these two perimeters as a fraction.
Step 2: Key Formula or Approach:
- The formula for the perimeter of a rectangle is \(P_R = 2(l + w)\), where \(l\) is the length and \(w\) is the width.
- The formula for the perimeter of a square is \(P_S = 4s\), where \(s\) is the side length.
- The required fraction is \(\frac{\text{Perimeter of S}}{\text{Perimeter of R}}\).
Step 3: Detailed Explanation:
Perimeter of Rectangle R:
Given length \(l = 30\) and width \(w = 10\).
\[ P_R = 2(30 + 10) = 2(40) = 80 \] Perimeter of Square S:
Given side length \(s = 5\).
\[ P_S = 4 \times 5 = 20 \] Fraction:
Now, we find the fraction of the perimeter of S to the perimeter of R.
\[ \text{Fraction} = \frac{P_S}{P_R} = \frac{20}{80} \] Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 20.
\[ \frac{20 \div 20}{80 \div 20} = \frac{1}{4} \] Step 4: Final Answer:
The perimeter of S is \(\frac{1}{4}\) of the perimeter of R.