Mathematics · Quantitative Aptitude

Triangle Properties

243 Questions

Triangle properties encompass the rules governing the sides, angles, and area of different types of triangles. Key areas include the Pythagorean theorem, similar triangles, and centroid calculations. These concepts form a foundational part of geometry in various competitive examinations.

Similar trianglesArea and perimeterPythagorean theoremTriangle inequalityEquilateral properties

Triangle Properties Questions

Multiple choice

In the 2020 China Girls' Mathematical Olympiad, what was the area of a triangle with sides of length 6 cm, 8 cm, and 10 cm?

  1. 24 cm^2

  2. 30 cm^2

  3. 36 cm^2

  4. 42 cm^2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the area of a triangle with sides of length a, b, and c, we can use Heron's formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle. In this case, s = (6 + 8 + 10) / 2 = 12. Plugging in the values a = 6, b = 8, and c = 10, we get Area = √(12(12-6)(12-8)(12-10)) = √(12 * 6 * 4 * 2) = 36 cm^2.

Multiple choice

In the 2008 China Girls' Mathematical Olympiad, what was the area of a triangle with base 12 cm and height 8 cm?

  1. 48 cm^2

  2. 64 cm^2

  3. 80 cm^2

  4. 96 cm^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a triangle with base b and height h is given by the formula A = (1/2)bh. Plugging in the values b = 12 and h = 8, we get A = (1/2)(12)(8) = 48 cm^2.

Multiple choice

Find the perimeter of a triangle with sides of length 6 cm, 8 cm, and 10 cm.

  1. 24 cm

  2. 26 cm

  3. 28 cm

  4. 30 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter of the given triangle is: $$Perimeter = 6 cm + 8 cm + 10 cm$$ $$Perimeter = 24 cm$$