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How to find the Length of one side of a Triangle?

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Geometry is a branch of mathematics concerned with the shape of individual objects, their spatial relationships, and the properties of surrounding space. It’s the study of items’ sizes, shapes, locations, angles, and measurements. From a tiny pin to a massive submarine, we are always surrounded by the geometry of various kinds and sizes. The shape and surface area of such forms must be evaluated in order to store them easily or suit the demands of those who will use them. In the subject of mathematics, such research or computation is given a specific name.

What is Mensuration?

Mensuration is a mathematical field that studies the calculation of geometric figures and their attributes such as area, length, volume, lateral surface area, surface area, and so on. It covers all of the key equations and properties of a wide range of geometric shapes and figures, as well as the foundations of computing.

Triangle

A triangle is defined by its three sides, three vertices, and three angles. The sum of a triangle’s three interior angles is always 180°. The sum of the lengths of a triangle’s two sides is always greater than the length of the third side. â–³ABC denotes a triangle with the vertices A, B, and C. A triangle’s area is equal to half of the product of its base and height.

Types of triangles

Triangles are divided according to their side lengths into the following categories:

  • Equilateral Triangle: An equilateral triangle has three sides that are of the same length.
  • Isosceles triangle: When two sides of a triangle are equal or congruent, an isosceles triangle is generated.
  • Scalene triangle: A scalene triangle is formed when none of the sides of a triangle are equal.

How to find the length of one side of a triangle?

Solution:

The length of one side of a triangle can be evaluated from the perimeter and area values of the triangle but the triangle must be equilateral.

Let us look at both the cases one by one.

Method 1: When the perimeter is given

The perimeter of a triangle is defined as the sum of its sides.

Let’s say there is an equilateral triangle with unknown side length a.

Then its perimeter(P) is, a + a + a = 3a.

3a = P

a = P/3

Method 2: When the area is given

The area of an equilateral triangle is given by, A=\frac{\sqrt{3}}{4}a^2  .

Solve the equation for unknown side length a.

a^2=\frac{4A}{\sqrt{3}}

a=\sqrt{\frac{4A}{\sqrt{3}}}

Sample Problems

Question 1. Find the side of an equilateral triangle with a perimeter of 24 units.

Solution:

Suppose the side length is a.

The perimeter of an equilateral triangle with side length a is 3a.

3a = P

3a = 24

a = 8

Question 2. Find the side of an equilateral triangle with a perimeter of 30 units.

Solution:

Suppose the side length is a.

The perimeter of an equilateral triangle with side length a is 3a.

3a = P

3a = 30

a = 10

Question 3. Find the side of an equilateral triangle with a perimeter of 45 units.

Solution:

Suppose the side length is a.

The perimeter of an equilateral triangle with side length a is 3a.

3a = P

3a = 45

a = 15

Question 4. Find the side of an equilateral triangle with a perimeter of 99 units.

Solution:

Suppose the side length is a.

The perimeter of an equilateral triangle with side length a is 3a.

3a = P

3a = 99

a = 33

Question 5. Find the side of an equilateral triangle with an area of 36√3 sq. units.

Solution:

Suppose the side length is a.

We have, A = 36√3

a^2=\frac{4(36√3)}{\sqrt{3}}

a2 = 144

a = 12

Question 6. Find the side of an equilateral triangle with an area of 16√3 sq. units.

Solution:

Suppose the side length is a.

We have, A = 16√3

a^2=\frac{4(16√3)}{\sqrt{3}}

a2 = 64

a = 8

Question 7. Find the side of an equilateral triangle with an area of 9√3 sq. units.

Solution:

Suppose the side length is a.

We have, A = 9√3

a^2=\frac{4(9√3)}{\sqrt{3}}

a2 = 36

a = 6


Last Updated : 22 Feb, 2022
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