Which of the following can be the third side of a triangle whose two side are 7 cm and 9 cm?

Solution:

Given, the length of two sides of a triangle are 18 cm and 14 cm.

We have to find the length of the third side of the triangle.

We know that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

Sum of two sides = 18 + 14

= 32 cm

We know that the third side must be greater than the difference between two sides and less than the sum of two sides.

Difference of two sides = 18 - 14

= 4 cm

So, the third side must be greater than 4 cm and less than 32 cm.

Therefore, the third side is 5 cm.

✦ Try This: Which of the following can be the length of the third side of a triangle whose two sides measure 12 cm and 25 cm

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6


NCERT Exemplar Class 7 Maths Chapter 6 Problem 31

Which of the following can be the length of the third side of a triangle whose two sides measure 18 cm and 14 cm? a. 4 cm, b. 3 cm, c. 5 cm, d. 32 cm

Summary:

The length of the third side of a triangle whose two sides measure 18 cm and 14 cm is 5 cm


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  • The measures of ∠x and ∠y in Fig. 6.14 are respectively: (a) 30°, 60°, (b) 40°, 40°, (c) 70°, 70°, ( . . . .

RS Aggarwal Solutions Class 9 Mathematics Solutions for Congruence Of Triangles And Inequalities In A Triangle Exercise 9B in Chapter 9 - Congruence Of Triangles And Inequalities In A Triangle

Question 1 Congruence Of Triangles And Inequalities In A Triangle Exercise 9B

Is it possible to construct a triangle with lengths of its sides as given below? Give reason for your answer.

(i) 5cm, 4cm, 9cm

(ii) 8cm, 7cm, 4cm

(iii) 10cm, 5cm, 6cm

(iv) 2.5cm, 5cm, 7cm

(v) 3cm, 4cm, 8cm

Answer:

(i) No. It is not possible to construct a triangle with lengths of its sides 5cm, 4cm and 9cm because the sum of two sides is not greater than the third side i.e. 5 + 4 is not greater than 9.

(ii) Yes. It is possible to construct a triangle with lengths of its sides 8cm, 7cm and 4cm because the sum of two sides of a triangle is greater than the third side.

(iii) Yes. It is possible to construct a triangle with lengths of its sides 10cm, 5cm and 6cm because the sum of two sides of a triangle is greater than the third side.

(iv) Yes. It is possible to construct a triangle with lengths of its sides 2.5cm, 5cm and 7cm because the sum of two sides of a triangle is greater than the third side.

(v) No. It is not possible to construct a triangle with lengths of its sides 3cm, 4cm and 8cm because the sum of two sides is not greater than the third side.

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The third side(C) of a triangle is in the range of |a - b| < C < |a + b|; where a and are the other two sides of the triangle.

Let the third side be 'c'.

∴ Minimum integral value of the third side is 3 cm.

Take modules both sides because the value of sides never be negative.

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Perimeter of Triangle: The perimeter of any two-dimensional figure is defined as the distance around the figure. We can calculate the perimeter of any closed shape just adding up the length of each of the sides. In this article, you will first learn about what is the perimeter, how to find the perimeter of different types of triangles when all side lengths are known. Furthermore, the solved examples will help you to get more views on the topic.

What is the Perimeter of a Triangle?

The sum of the lengths of the sides is the perimeter of any polygon. In the case of a triangle,

Perimeter = Sum of the three sides

Always include units in the final answer. If the sides of the triangle are measured in centimetres, then the final answer should also be in centimetres.

Perimeter of Triangle Formula

The formula for the perimeter of a closed shape figure is usually equal to the length of the outer line of the figure. Therefore, in the case of a triangle, the perimeter will be the sum of all the three sides. If a triangle has three sides a, b and c, then,

Perimeter, P = a + b +c

Perimeter of an Isosceles, Equilateral and Scalene Triangle

Below table helps us to understand how to find the perimeter of different triangles- Equilateral triangle, Isosceles triangle and Scalene triangle.

Where a, b, c and l are the side lengths and P = Perimeter.

This formula implies to find the perimeter of a triangle, add the lengths of all of its 3 sides together. If A, B and C are the side measures, and X is perimeter then

Perimeter of Right Triangle

A right triangle has a base(b), hypotenuse(h) and perpendicular(p) as its sides, By the Pythagoras theorem, we know,

h2 = b2 + p2

Therefore, the Perimeter of a right angle triangle= b + p + h

Video Lesson on Triangles

Solved Examples

Let us consider some of the examples on the perimeter of a triangle:

Example 1: Find the perimeter of a polygon whose sides are 5 cm, 4 cm and 2 cm.

Solution: Let,

a = 5 cm

b = 4 cm

c = 2 cm

Perimeter = Sum of all sides = a + b + c = 5 + 4 + 2 = 11

Therefore, the answer is 11 cm.

Example 2: Find the perimeter of a triangle whose each side is 10 cm.

Solution: Since all three sides are equal in length, the triangle is an equilateral triangle.

i.e. a = b = c = 10 cm

Perimeter = a + b + c

= 10 + 10 + 10

= 30

Perimeter = 30 cm. 

Example 3: What is the missing side length of a triangle whose perimeter is 40 cm and two sides are 10 cm each?

Solution: Given,

Perimeter = 40 cm

Length of two sides is the same i.e. 10 cm.

Thus, the triangle is an isosceles triangle.

Using formula: P = 2l + b

40 = 2 * 10 + b

40 = 20 + b

or b = 20

Missing side length is 20 cm.

To learn more about triangles and related topics in Geometry, register with BYJU’S today and sharpen your skills.

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Frequently Asked Questions

What does the Perimeter of a Triangle Mean?

The perimeter of a triangle is the total distance around the edges of a triangle. In other words, the length of the boundary of a triangle is its perimeter.

How to Calculate the Perimeter of a Triangle?

To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.

Calculate the Perimeter of a Right Triangle with Base as 3 cm and height as 4 cm.

First, using the Pythagorean theorem, calculate the hypotenuse of the right triangle.

h =√(base2+perpendicular2)

h = √(32+42)

h = √(9 + 16)

h = √25

Or, h = 5 cm

So, the perimeter of the triangle = 3 + 4 + 5 = 12 cm.

How to calculate the perimeter of a scalene triangle?

If x, y, and z are the sides of a scalene triangle, then its perimeter formula is given by:
Perimeter of a scalene triangle, P = x + y + z units.

What is the formula for the perimeter of an isosceles triangle?

As we know that the isosceles triangle has 2 equal sides, then the formula for the perimeter of an isosceles triangle is given as P = 2x + y units,
where “x” is the measure of equal sides of a triangle and “y” is the third side.

What is the formula for the perimeter of an equilateral triangle?

In an equilateral triangle, all the sides are equal. Let the side length of an equilateral triangle be “x”.
Thus, the perimeter of an equilateral triangle is = 3x units.

Calculate the perimeter of an equilateral triangle if its side measures 5 cm.

Given: Side measure of equilateral triangle = 5 cm.
Now, substitute the side value in the perimeter of an equilateral triangle formula, we get
P = 3 (5) = 15 units.

Find the perimeter of a triangle whose sides are 3 cm, 4 cm and 6 cm.

We know that the perimeter of a triangle = x + y + z units
Hence, P = 3 + 4 + 6 = 13 cm.

So, the length of the third side must lie between 2 cm and 16 cm.

We know that, The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. The difference in the lengths of any two sides of a triangle is always smaller than the length of the third side. Therefore, 5 cm is the length of the 3rd side.

Therefore, the third side of a triangle can be 5cm. Was this answer helpful?

∴ Minimum integral value of the third side is 3 cm.

Which of the following can be the third side of triangle if two sides are 9cm 6cm?

We know that, The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. The difference in the lengths of any two sides of a triangle is always smaller than the length of the third side. Therefore, 5 cm is the length of the 3rd side.

How do you find a third side of a triangle given two sides?

(Perpendicular)2 + (Base)2 = (Hypotenuse)2 Using the above equation third side can be calculated if two sides are known.

Which of the following can be the third side of a triangle whose two sides are 7 cm and 10cm respectively?

Thus, 3 cm < third side <17 cm.

Which of the following can be the third side of a triangle whose two sides are 8cm and 5cm respectively?

Therefore, the third side of a triangle can be 5cm. Was this answer helpful?