Multiple choice

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities. Quantity I: Area of a right triangle with base as 16 cm and hypotenuse as 4 cm more than base Quantity II: Area of a square with side 9 cm

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II, or No relation
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A Correct answer
Explanation

Quantity I: Base = 16, Hypotenuse = 16+4 = 20. Height = sqrt(20^2 - 16^2) = sqrt(400 - 256) = sqrt(144) = 12. Area = 1/2 * 16 * 12 = 96. Quantity II: Area = 9^2 = 81. Since 96 > 81, Quantity I > Quantity II.

AI explanation

Using the Pythagorean theorem for the right triangle, the perpendicular height is the square root of (20 squared minus 16 squared), which equals 12 centimeters. The area of this right triangle is found by the formula half multiplied by base multiplied by height, giving 0.5 times 16 times 12, which equals 96 square centimeters. The area of the square is 9 squared, which equals 81 square centimeters. Comparing the two values, 96 is greater than 81.

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