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Home » Altogether vs All Together: Is One the Ultimate Setup for Conflict? - Abbey Badges

Altogether vs All Together: Is One the Ultimate Setup for Conflict? - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 #### 0.148 (approximately)

📌 The sum of three consecutive even integers is 84. What is the product of the smallest and largest of these integers?

📌 Let the integers be x, x+2, x+4. Their sum is 3x + 6 = 84 → 3x = 78 → x = 26.

📌 The numbers are 26, 28, and 30.

📌 The product of the smallest and largest is 26 × 30 = 780.

📌 A rectangle has a length that is 3 times its width. If the diagonal is 10√10 meters, what is the area of the rectangle?

📌 By Pythagoras: w² + (3w)² = (10√10)² → w² + 9w² = 1000 → 10w² = 1000 → w² = 100 → w = 10.

📌 Length = 30, so area = 10 × 30 = 300 square meters.

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