Advanced MathVery hardArea of a rectangle from its diagonal and perimeter
Advanced Math practice question
A rectangle has a diagonal of length 13 and a perimeter of 34. What is the area of the rectangle?
Answer: 60
Let the sides be l and w: l + w = 17 and l² + w² = 169. Since (l + w)² = l² + w² + 2lw, 289 = 169 + 2lw, so lw = 60. (The sides are 12 and 5.)
Common wrong answers
- If you answered 30
- 30 halves the area a second time.
- If you answered 120
- 120 is 2lw, forgetting to halve.
- If you answered 221
- 221 is 13 × 17, multiplying the given numbers.
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