SUMMARY
The perimeter of a rectangle with a 3:2 ratio and an area of 294 dm² can be calculated using the formulas for area and perimeter. Given the ratio, let the length (L) be 3x and the width (W) be 2x. The area equation becomes 3x * 2x = 294, leading to x² = 49, thus x = 7. Consequently, the dimensions are L = 21 dm and W = 14 dm, resulting in a perimeter of 70 dm, calculated as 2*(L + W).
PREREQUISITES
- Understanding of basic geometry concepts, specifically rectangles.
- Knowledge of algebraic manipulation to solve equations.
- Familiarity with the formula for area (A = L * W).
- Ability to calculate perimeter using the formula P = 2*(L + W).
NEXT STEPS
- Study the properties of similar triangles to understand ratios better.
- Learn how to derive equations from geometric relationships.
- Explore more complex area and perimeter problems involving different shapes.
- Practice solving algebraic equations involving multiple variables.
USEFUL FOR
Students learning geometry, educators teaching mathematical concepts, and anyone interested in solving practical problems involving area and perimeter of rectangles.