Multiple choice

The height of a triangle ranges from 7 to 11 centimeters and the length of the base ranges from 4 centimeters to 9 centimeters. Quantity A The greatest possible area of the triangle Quantity B Area of a circle whose radius is 3 centimeters.

  1. Quantity A is greater.

  2. Quantity B is greater

  3. The two quantities are equal

  4. The relationship cannot be established from the information given
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The maximum area of a triangle is (1/2) * base * height. Using the maximum values (base=9, height=11), the area is 0.5 * 9 * 11 = 49.5. The area of a circle with radius 3 is pi * r^2 = 3.14 * 9 = 28.26. Since 49.5 > 28.26, Quantity A is greater.

AI explanation

The greatest possible area of the triangle uses the maximum dimensions, so base = 9 cm and height = 11 cm. Using the triangle area formula, one-half times base times height, the area is one-half times 9 times 11, which equals 49.5 cm2. The area of the circle is pi times 3 squared, which is about 28.27 cm2. Since 49.5 is greater than 28.27, Quantity A is greater.

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