Mathematics ยท 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

What is the area of a triangle with base 10 and height 8?

  1. 40

  2. 50

  3. 60

  4. 70
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a triangle is given by the formula $A = (1/2)bh$. Substituting the given values, we get $A = (1/2)(10)(8) = 40$.

Multiple choice

What is the name of the theorem that states that the area of a triangle is equal to half the product of its base and height?

  1. Pythagorean theorem

  2. Brahmagupta theorem

  3. Angle sum theorem

  4. Heron's formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Heron's formula states that the area of a triangle is equal to half the product of its base and height.

Multiple choice

What is the name of the theorem that states that the area of a triangle is equal to half the product of its base and height?

  1. Pythagorean theorem

  2. Brahmagupta theorem

  3. Angle sum theorem

  4. Heron's formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Heron's formula states that the area of a triangle is equal to half the product of its base and height.

Multiple choice

What is the name of the theorem that states that the area of a triangle is equal to half the product of its base and height?

  1. Pythagorean Theorem

  2. Brahmagupta's Theorem

  3. Euclid's Theorem

  4. Heron's Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Heron's Formula is a well-known formula for finding the area of a triangle.

Multiple choice

What is the name of the theorem that states that the area of a triangle is equal to half the product of its base and height?

  1. Pythagorean Theorem

  2. Brahmagupta's Theorem

  3. Euclid's Theorem

  4. Heron's Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Heron's Formula is a well-known formula for finding the area of a triangle.

Multiple choice

What is the name of the theorem that states that the area of a triangle is equal to half the product of its base and height?

  1. Pythagorean theorem

  2. Triangle inequality theorem

  3. Euler's theorem

  4. Heron's formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Heron's formula states that the area of a triangle is equal to half the product of its base and height. This formula is named after Heron of Alexandria, who first discovered it in the 1st century AD.

Multiple choice

What is the name of the theorem that states that the area of a triangle is equal to half the product of its base and height?

  1. Pythagorean theorem

  2. Triangle inequality theorem

  3. Euler's theorem

  4. Heron's formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Heron's formula states that the area of a triangle is equal to half the product of its base and height. This formula is named after Heron of Alexandria, who first discovered it in the 1st century AD.

Multiple choice

Brahmagupta's formula for finding the area of a triangle is:

  1. $A = \frac{1}{2}bh$
  2. $A = \frac{1}{2}ab$
  3. $A = \frac{1}{2}bc$
  4. $A = \frac{1}{2}ca$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for finding the area of a triangle is $A = \frac{1}{2}bh$.

Multiple choice

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

  1. 24 cm^2

  2. 36 cm^2

  3. 48 cm^2

  4. 60 cm^2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the area of a triangle with sides of length 6 cm, 8 cm, and 10 cm, we can use Heron's formula: (A = \sqrt{s(s-a)(s-b)(s-c)}), where (s) is the semiperimeter of the triangle and (a, b, c) are the lengths of the sides. Plugging in the values of (a = 6, b = 8, c = 10), we get (s = \frac{6 + 8 + 10}{2} = 12). Therefore, (A = \sqrt{12(12-6)(12-8)(12-10)} = \sqrt{12(6)(4)(2)} = 36) cm^2.

Multiple choice

Brahmagupta's formula for finding the area of a triangle is given by: $K = \frac{1}{2} \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter and $a$, $b$, and $c$ are the lengths of the sides of the triangle. This formula is also known as:

  1. Brahmagupta's Triangle Formula

  2. Brahmagupta's Heron's Formula

  3. Brahmagupta's Pythagorean Theorem

  4. Brahmagupta's Area Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Brahmagupta's area formula is a mathematical equation that gives the area of a triangle in terms of the lengths of its sides.

Multiple choice

What formula did Dandin provide for the area of a triangle?

  1. $\frac{1}{2}bh$
  2. $\frac{1}{2}ab$
  3. $\frac{1}{2}ac$
  4. $\frac{1}{2}bc$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Dandin gave the formula for the area of a triangle as (\frac{1}{2}bh), where (b) is the base and (h) is the height.

Multiple choice

What is Bhaskara II's formula for finding the area of a triangle?

  1. $\frac{1}{2} * base * height$
  2. $\frac{1}{2} * base^2 * height$
  3. $\frac{1}{2} * base * height^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Bhaskara II's formula for finding the area of a triangle is (\frac{1}{2} * base * height).

Multiple choice

What is the formula for calculating the area of a triangle using Bhaskara's formula?

  1. $$Area = \sqrt{s(s - a)(s - b)(s - c)}$$
  2. $$Area = \frac{1}{2}absinC$$
  3. $$Area = \frac{1}{2}bh$$
  4. $$Area = \frac{1}{2}lw$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Bhaskara's formula for calculating the area of a triangle is given by the formula $$Area = \sqrt{s(s - a)(s - b)(s - c)}$$, where 's' is the semi-perimeter of the triangle and 'a', 'b', and 'c' are the lengths of its sides.

Multiple choice

What is the formula for calculating the area of a triangle using Aryabhata's formula?

  1. $$Area = \sqrt{s(s - a)(s - b)(s - c)}$$
  2. $$Area = \frac{1}{2}absinC$$
  3. $$Area = \frac{1}{2}bh$$
  4. $$Area = \frac{1}{2}lw$$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Aryabhata's formula for calculating the area of a triangle is given by the formula $$Area = \frac{1}{2}bh$$, where 'b' is the length of the base of the triangle and 'h' is the height of the triangle.

Multiple choice

In a triangle, the ratio of the lengths of two sides is 3:4. If the perimeter of the triangle is 42 cm, find the length of the longest side.

  1. 18 cm

  2. 20 cm

  3. 22 cm

  4. 24 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the lengths of the two sides be 3x cm and 4x cm. Then, the third side has length (42 - 3x - 4x) cm = (42 - 7x) cm. Since the perimeter of the triangle is 42 cm, we have 3x + 4x + (42 - 7x) = 42. Solving for x, we get x = 6. Therefore, the length of the longest side is 4x cm = 4 * 6 cm = 24 cm.