Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. I- In a triangle PQR, PQ=15cm, QR= 9cm and PR=12cm. The length of the median bisecting the shortest side is___? II- The three sides of a triangle measure 15cm, 9cm and 12cm respectively. A rectangle equal in area to the triangle and has a length of 9cm. The perimeter of rectangle is _____?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: In triangle with sides 15, 9, 12, the median to shortest side (9cm) is calculated using Apollonius theorem: m = √(2a² + 2b² - c²)/2 = √(2×225 + 2×144 - 81)/2 = 13.5cm. Quantity II: Area = √(18×3×6×9) = 54cm² using Heron's formula. For equal area rectangle with length 9, width = 6, so perimeter = 2(9+6) = 30cm. Since 13.5 < 30, Quantity II > Quantity I.

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