16Hit1600
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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