The perimeter of a triangle is 8 + 13a + 7a² and two of its sides are 2a² + 3a + 2 and 3a² - 4a - 1. Find the third side of the triangle.
Algebraic Expressions
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Question

The perimeter of a triangle is 8 + 13a + 7a2 and two of its sides are 2a2 + 3a + 2 and 3a2 - 4a - 1. Find the third side of the triangle.

KnowledgeBoat · Accepted Answer

Given: Perimeter of a triangle = 8 + 13a + 7a2 Side 1 (S1) = 2a2 + 3a + 2 Side 2 (S2) = 3a2 - 4a - 1 Side 3 (S3) = ? We know the formula, Perimeter of a triangle = S1 + S2 + S3 S3 = Perimeter of a triangle - (S1 + S2) Substituting the values above, we get: S3 = (8 + 13a + 7a2) - ((2a2 + 3a + 2) + (3a2 - 4a - 1)) First, let's find S1 + S2: Sum (S1 + S2) = 1 - a + 5a2 Now, we have S3 = (8 + 13a + 7a2) - (1 - a + 5a2) Subtract Sum (S1 + S2) from perimeter of a triangle: S3 = 7 + 14a + 2a2 ∴ The third side of the triangle is 7 + 14a + 2a2.

Mathematics

The perimeter of a triangle is 8 + 13a + 7a² and two of its sides are 2a² + 3a + 2 and 3a² - 4a - 1. Find the third side of the triangle.

Algebraic Expressions

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