Question

the perimeter of a triangle is (7x²-17xy+15y²+8) and the two sides are (3x²-6xy+4y²-5) and (2a²-9xy+6y²+6). Find the third side of a triangle​

Answer 1

Answer:-

Given:-

• Perimeter of the triangle = (7x² - 17xy + 15y² + 8) units
• Two sides:-

1. (3x² - 6xy + 4y² - 5) units
2. (2a² - 9xy + 6y² + 6) units

To Find:-

Measurement of the third side.

____________...

Let the measurement of the third side be = β

We know,

Perimeter of Triangle = Total measurement of the three sides.

According to the Question:-

(3x² - 6xy + 4y² - 5) + (2a² - 9xy + 6y² + 6) + β = 7x² - 17xy + 15y² + 8

⟹ 3x² - 6xy + 4y² - 5 + 2a² - 9xy + 6y² + 6 + β = 7x² - 17xy + 15y² + 8

⟹ 3x² - 6xy - 9xy + 4y² + 6y² + 2a² + 6 - 5 + β = 7x² - 17xy + 15y² + 8

⟹ 3x² - 15xy + 10y² + 2a² + 1 + β = 7x² - 17xy + 15y² + 8

⟹ β = (7x² - 17xy + 15y² + 8) - (3x² - 15xy + 10y² + 2a² + 1)

⟹ β = 7x² - 17xy + 15y² + 8 - 3x² + 15xy - 10y² - 2a² - 1

⟹ β = 7x² - 3x² - 17xy + 15xy + 15y² - 10y² - 2a² + 8 - 1

⟹ β = 4x² - 2xy + 5y² - 2a² + 7

∴ The third side was (4x² - 2xy + 5y² - 2a² + 7) units.