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 general knowledge math & puzzles

The sides of a triangle are 5, 12 and 13 units respectively. A rectangle is constructed which is equal in area to the triangle and has a width of 10 units. Then the perimeter of the rectangle is

  1. 30

  2. 26

  3. 13

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The triangle is a right triangle (5-12-13). Area = 0.5 * 5 * 12 = 30. A rectangle with area 30 and width 10 must have length 3 (30/10). The perimeter of the rectangle is 2 * (length + width) = 2 * (10 + 3) = 26.

Multiple choice general knowledge math & puzzles

Find, in square cm, the area of an equilateral triangle of side 20 cm

  1. 200?3

  2. 100?3

  3. 50?3

  4. 400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of an equilateral triangle with side s is A = (√3/4)s². Substituting s = 20 cm: A = (√3/4)(20)² = (√3/4)(400) = 100√3 square cm. Option A (200√3) would be for a triangle with side 28.28 cm, Option C (50√3) would be for side 14.14 cm, and Option D (400) would be for an equilateral triangle with approximately side 30.3 cm or could be the result of forgetting the √3/4 factor.

Multiple choice general knowledge math & puzzles

The two legs of a right triangle measure 6 and 8 inches respectively. What is the area of the circle that contains all 3 vertices of the triangle?

  1. 24Pi

  2. 25Pi

  3. 36Pi

  4. 64Pi
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a right triangle, the circle containing all vertices is the circumcircle, and its diameter is the hypotenuse. Using the Pythagorean theorem (6^2 + 8^2 = 10^2), the hypotenuse is 10. The radius is 5, so the area is Pi * 5^2 = 25Pi.

Multiple choice general knowledge math & puzzles

You have been given two similar triangles, MNO and DEF. You have to find out the ratios of their areas. Which of the following formulae can be used to find out the ratio of the areas of the given triangles.

  1. The ratio of the areas of the triangles is equal to the square of the corresponding sides

  2. The ratio of the areas of the triangles is equal to the square of the corresponding altitudes

  3. The ratio of the areas of the triangles is equal to the square of the corresponding medians

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For similar triangles, the ratio of areas is the square of the ratio of ANY corresponding linear dimensions - sides, altitudes, medians, or perimeters. However, the most fundamental and commonly stated version uses the sides directly.

Multiple choice general knowledge math & puzzles

What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?

  1. 6.5

  2. 12

  3. 2

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The triangle with sides 5, 12, 13 is a right triangle since 5² + 12² = 13². For any triangle, the inradius r = A/s where A is the area and s is the semi-perimeter. Here, s = (5+12+13)/2 = 15 and A = (5×12)/2 = 30, so r = 30/15 = 2 units. Options A (6.5) and D (6) are not the inradius; B (12) is the longest side, not the inradius.

Multiple choice general knowledge math & puzzles

If the midpoints of all the sides of the equilateral triangle are connected, and this process is repeated 3 more times with the resulting triangle from the previous step, then the area of the final triangle is 1/256 the original area.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Connecting the midpoints of an equilateral triangle creates a central triangle with 1/4 the area of the original. Repeating this process 3 more times (4 times total) results in an area of (1/4)^4 = 1/256 of the original area. Thus, the statement is true.

Multiple choice

Triangle 1 has length of sides as 30 m, 40 m and 50 m respectively. Triangle 2 has length of sides as 25 m, 35 m and 60 m respectively. Which triangle has the bigger area?

  1. Triangle 1

  2. Triangle 2

  3. Both triangles have the same area

  4. Both the triangles can have any number of areas as no angles are specified

  5. Data insufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

It is impossible to have a triangle with lengths of sides as given for triangle 2. Hence, triangle 1 has a bigger area.

Multiple choice

In an isosceles triangle, two equal sides are each 8 cm less than three times the third side. The perimeter of triangle is 33 cm. What is the measurement of equal sides?

  1. 7 cm

  2. 8.2 cm

  3. 13 cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the third side is = x 

 Three times of x is = 3x  8 cm less than 3 times = ( 3x - 8 ) cm  two equal sides are = ( 3x - 8 ) cm Perimeter of of triangle is sum of all sides                   ( 3x - 8 ) + ( 3x -  8 ) + x = 33                     3x - 8 + 3x - 8 + x = 33                                        3x + 3x + x - 8 - 8 = 33                                         7x - 16 = 33                                             7x = 33 + 16                                           7x = 49                              x = 49 / 7                                         x = 7 cm                        Third side is 7 cm                    Two equal sides are =( 3 x 7 ) - 8                                               = 21 - 8                                                = 13 cm                                                    Two equal sides measure = 13 cm each