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 maths area of complex plane figures 2d and 3d figures

Find the area of equilateral  triangle inscribed in a circle of unit radius.

  1. 3/4
  2. $\dfrac {3\sqrt { 3 } }{4}$

  3. 3
  4. $\frac { 3\sqrt { 3 } }{ 2 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The radius of circumcircle  of equilateral triangle is  $\dfrac 23h=1\h=\dfrac 32$

The side of equilateral triangle is given as $\dfrac{4h}{\sqrt 3} \\dfrac{4}{\sqrt 3}\times \dfrac 32=2\sqrt 3$ 
The area of triangle is given as $\dfrac {\sqrt 3}{4}(2\sqrt 3)^2=3\sqrt 3$

Multiple choice maths area of complex plane figures 2d and 3d figures

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

  1. 30 units

  2. 26 units

  3. 13 units

  4. 15 units
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By Pythagoras theorem, we find that the given triangle is a right angled triangle with $12$ as height and 5 as base. 
$\displaystyle \therefore $ Area of the triangle $\displaystyle =\frac{1}{2}\times12\times5sq. units$
= $30$ sq. units
$\displaystyle \therefore $ Area of the rectangle = $length \times breadth$ = $30$
$\displaystyle \Rightarrow Length =\frac{30}{breadth}=\frac{30}{10}=3\, units$
$\displaystyle \therefore $ Perimeter of the rectangle  = $2 \times ( 10 + 3 ) $Units 
= $26$ units.

Multiple choice maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

The base of a right prism is an equilateral triangle of edge $12$m. If the volume of the prism is $288\sqrt 3m^3$, then its height is:

  1. $6$m
  2. $8$m
  3. $10$m
  4. $12$m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

length of Equilateral triangle $= 12 m$
Area of equilateral triangle = $\displaystyle \frac{\sqrt{3}}{4}a^2$ = $\displaystyle \frac{\sqrt{3}}{4}(12)^2$ = $36\sqrt{3}$
Volume of prism = $288\sqrt{3} m^3$ = Area of triangle X height
$288\sqrt{3} m^3$ = $36 \sqrt{3} \times$ height
$\therefore $ Height $= 8 m$

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

Two sides of a triangle are of lengths 5 cm and 1.5 cm, then the length of the third side of the triangle cannot be

  1. $\displaystyle3.6\,cm$
  2. $\displaystyle4.1\, cm$
  3. $\displaystyle3.8\, cm$
  4. $\displaystyle3.4\, cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a triangle, the difference between two sides should be less than the third side.
Hence,option D is correct $3.4\ cm$

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

Which of the following sets of side lengths form a triangle?

  1. 4 m, 3 m, 11 m

  2. 7 mm, 4 mm, 4 mm

  3. 3 cm, 1.23 cm, 5 cm

  4. 3 m, 10 m, 8 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A triangle can be formed only if sum of any two sides is greater than the third side.

In option $C$ sum of any two sides taken a time is greater than the third side.
$7+4>4$
$4+4>7$
$4+7>4$
So option $C$ is correct.

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

It is not possible to construct a triangle with which of the following sides?

  1. $8.3\ cm, 3.4\ cm, 6.1\ cm$
  2. $5.4\ cm, 2.3\ cm, 3.1\ cm$
  3. $6\ cm, 7\ cm, 10\ cm$
  4. $3\ cm, 5\ cm, 5\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A triangle can be formed only if sum of any two sides is greater than the third side.

In option $C$
$2.3cm+3.1cm=5.4cm$
which is equal to the third side.
So a triangle can not be constructed.

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

It is not possible to construct a triangle when its sides are :

  1. 8.3 cm, 3.4 cm, 6.1 cm

  2. 5.4 cm, 2.3 cm, 3.1 cm

  3. 6 cm, 7 cm, 10 cm

  4. 3 cm, 5 cm, 5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For forming a triangle sum of any two sides must be greater than the third side.

In option $B$
$2.3cm+3.1cm=5.4cm$
which is equal to the third side.
So a triangle can not be formed.
Option $B$ is correct.

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

If length of the largest side of a triangle is 12 cm then other two sides of triangle can be :

  1. 4.8 cm, 8.2 cm

  2. 3.2 cm, 7.8 cm

  3. 6.4 cm, 2.8 cm

  4. 7.6 cm, 3.4 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of any two sides of a triangle is greater than the third side.

Here the sum must be greater than $12\ \ cm$
In option $A$
$4.8\ \ cm+8.2\ \ cm=13\ \ cm$
$\Rightarrow 13\ \ cm>12 \ \ cm$
In rest of the options sum is less than $12\ \ cm$
So option $A$ is correct. 

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

Out of isosceles triangles with sides of 7 cm and a base with the length expressed by whole number, the triangle with the greatest perimeter was selected. This perimeter is equal to.......

  1. 14 cm

  2. 15 cm

  3. 21 cm

  4. 27 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Since sum of the two sides is greater than the third side.

$7+7>x$    [for a triangle]

for max perimeter, $x=13$

$\therefore$   perimeter $=7+7+13=27\ cm$