Find the lengths of the base of a triangle when one side is 2 cm shorter than the base and the other side is 3 cm longer than the base. the perimeter is greater than 19 cm

The length of base of triangle must be greater than 6 cm

Solution:

Let "b" be the base of triangle

Let "a" and "c" be the two sides of triangle

Given that one side is 2 cm shorter than the base

one side = 2 cm shorter than base

a = b - 2   eqn 1

Also given that other side is 3 cm longer than the base

other side = 3 cm longer than the base

c = 3 + b eqn 2

The perimeter of triangle is given as:

P = a + b + c eqn 3

Given that perimeter is greater than 19 cm

P > 19

Substitute eqn 1 and eqn 2 in eqn 3

b - 2 + b + 3 + b > 19

3b + 1 > 19

3b > 19 - 1

3b > 18

Divide both sides by 3

b > 6

Thus length of base of triangle must be b > 6 cm

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step-by-step explanation:

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