(i) Define the term ‘semi-perimeter’ of a triangle whose side lengths are , , and .…

MATHEMATICS · Subjective · CBSE · Mathematics · Heron's Formula · Heron's Formula

Problem

(i) Define the term ‘semi-perimeter’ of a triangle whose side lengths are

a

b

, and

c

. (ii) Without calculating any area, explain why each of the three quantities

(s-a)

(s-b)

, and

(s-c)

must be positive for any triangle that can actually be constructed from the side lengths

a

b

, and

c

. (iii) A triangle is said to have side lengths

4\,\text{cm}

7\,\text{cm}

, and

10\,\text{cm}

. Calculate its semi-perimeter and state whether the three quantities in part (ii) are all positive. What does your observation tell you about the possibility of forming a triangle with these three side lengths?

Related theory

Properties of Triangles
Triangle Properties
Heron's Formula
Area of Triangles
Triangle area and perimeter
Mensuration

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