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Length of a side of an equilateral triangle and its perimeter vary inversely with each other. State whether the statement is true (T) or false (F)

Solution:

The Statement if False(F).

If the side of the equilateral triangle is s then its perimeter is 3s i.e.

Perimeter(P) = 3s

It is evident from the above expression that the perimeter of the equilateral triangle is directly proportional to the length of the side of the equilateral triangle.

As s increases (↑) the perimeter also increases(↑) and as length of the side decreases(↓) the perimeter also decreases(↓).

Hence the perimeter of the equilateral triangle is directly proportional to the length of its side.

✦ Try This: What is the perimeter of the equilateral triangle with length of the side being as follows: (a) 6 cm (b) 8 cm and (c ) 4 cm

If the side of the equilateral triangle is s then its perimeter is 3s i.e.

Perimeter(P) = 3s

(a) When s = 6cm

Perimeter = 3s = 3 × 6 = 18 cm

(b) When s = 8cm

Perimeter = 3s = 3 × 9 = 24 cm

(c ) When s = 4cm

Perimeter = 3s = 3 × 4 = 12 cm

Hence it is evident from above that as s decreases(↓) the perimeter decreases(↓) while as s increases(↑) the perimeter increases(↑). Hence P and s are varying directly with each other.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 47

Length of a side of an equilateral triangle and its perimeter vary inversely with each other. State whether the statement is true (T) or false (F)

Summary:

Length of a side of an equilateral triangle and its perimeter vary inversely with each other - is a false (F) statement

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