The perimeter of the triangle is 6a + 3 units. Write an expression in simplest form for the length of Side 3.

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akposevictor akposevictor · Answer 1 · 2020-10-31T01:12:07+01:00

Answer:

Side 3 = a - 2

Step-by-step explanation:

Perimeter of a ∆ = sum of all the sides of a triangle

Perimeter of the given ∆ = 6a + 3 units

Side 1 = 2(a + 3)

Side 2 = 3a - 1

Side 3 = ?

Therefore:

Side 3 = Perimeter - sum of side 1 and 2

Thus:

Side 3 = 6a + 3 - [2(a + 3) + (3a - 1)]

Side 3 = 6a + 3 - [2a + 6 + 3a - 1]

Side 3 = 6a + 3 - [5a + 5]

Side 3 = 6a + 3 - 5a - 5

Side 3 = a - 2

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astha8579 astha8579 · Answer 2 · 2022-01-07T11:04:50+01:00

The length of the third side is a-2.

Given that:

Perimeter of triangle: 6a + 3

Length of first side: 2(a+3)

Length of second side: 3a -1

Let the length of the third side of the triangle be x.

Then as perimeter of a triangle is sum of lengths of all 3 sides of the triangle, thus we have:

[tex]2(a+3) + x + 3a -1 = 6a + 3\\\\x = 6a - 2a - 3a + 3 - 6 + 1\\\\x = a - 2[/tex]

Thus we have length of the third side as a -2.

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