Question

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if the length of two sides of triangle are 4 cm and 8 cm what is the length of third side?
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Answer 1

Answer:

In triangle sum of 2 sides must be greater than the 3rd side. So, the third > 8 - 6 = 2 and also the third < 8 + 6 = 14. So, the answer is 2 < third side < 14. The third side lies between(2,14).

Step-by-step explanation:

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Answer 2

★ Concept :-

Here the concept of Sides of Triangles has been used. We see that we are given the two sides of triangle and we are unknown to the third side of the triangle. We already have the rule of formation of triangle. Firstly we can describe the rules and understand them. Then we can apply those rules in the formation of third side and then find the answer.

Let's do it !!

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★ Solution :-

Given,

» Length of first side of Triangle = 4 cm

» Length of second side of Triangle = 8 cm

• Let the third side of triangle be 'x'

Let's solve this question, by step - by - step method.

• Step I ::

In this step we shall firstly understand the properties of formation of triangle and then analyse them.

✒ Property (A) : The sum of any two sides of the triangle should never be less than the third side of the triangle.

✒ Property (B) : The difference of any two sides of the triangle should never be greater than the third side of the triangle.

This means, the value of x will be such that it will be greater than difference of two sides and less than sum of two sides.

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• Step II ::

In this step, we shall find the difference and sum of the two sides of triangle. Then,

→ Difference of two sides = D = 8 - 4 = 4 cm

→ Sum of two sides = S = 8 + 4 = 12 cm

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• Step III ::

Here we shall find the possible values of third side of triangle. From above properties, we get

→ Difference (two sides of ∆) < x < Sum (two sides of ∆)

By applying values here, we get

→ 4 < x < 12

This means the value of x should be greater than 4 but less than 12.

This is the answer.

› Value of x = 4 < x < 12

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★ More to know :-

• Angle Sum Property of ∆ : This states that the sum of all the angles of triangle equal to 180° .

• Exterior Angle Property of ∆ : This states that the exterior angle of a triangle is equal to the sum of opposite two interior angles of the triangle.

• Acute Triangle : Triangle whose all the angles are less than 90° is called as acute triangle.

• Obtuse Triangle : Triangle whose any one angle exceeds 90° is called as obtuse triangle.

• Right Triangle : Triangle whose any one angle equals to 90° is called right triangle.