Question
Quantity-I: The area of a triangle is 72 cm². The base
of the triangle is 12 cm. Find the height of the triangle. Quantity-II: The area of a rectangle is 96 cm². The length of the rectangle is 16 cm. Find the width of the rectangle. Quantity-III: The area of a square is 100 cm². Find the side of the square. Which of the following pair of symbols will define the relation between Quantity I and Quantity II and between Quantity II and Quantity III respectively? A. = B. > C.Solution
Solution: Quantity I: Area of triangle = (1/2) × base × height 72 = (1/2) × 12 × height 72 = 6 × height height = 72 / 6 = 12 cm Quantity II: Area of rectangle = length × width 96 = 16 × width width = 96 / 16 = 6 cm Quantity III: Area of square = side² 100 = side² side = √100 = 10 cm Comparing Quantity-I, Quantity-II, and Quantity-III: Quantity-I = 12 cm Quantity-II = 6 cm Quantity-III = 10 cm Now, comparing: Quantity-I > Quantity-III < Quantity-II Therefore, the correct pair of symbols is: B & C Correct option: d
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