Question

9.
4M
The perimeter of a triangle is 7x2-17xy+5y2+8 and two of its sides
are 4x2-7xy+4y2-3 and 5+6y2-8xy+x2. Find the third side of the
triangle​

Answer 1

Answer:

9.

4M

The perimeter of a triangle is 7x2-17xy+5y2+8 and two of its sides

are 4x2-7xy+4y2-3 and 5+6y2-8xy+x2. Find the third side of the

triangle

Answer 2

$\sf \Large Solution!!$

Perimeter of triangle = Sum of all three sides of triangle

Perimeter = 7x² - 17xy + 5y² + 8

One side = 4x² - 7xy + 4y² - 3

Second side = 5 + 6y² - 8xy + x²

We have to find the third side of the triangle.

Perimeter = Side A + Side B + Side C

→ (7x² - 17xy + 5y² + 8) = (4x² - 7xy + 4y² - 3) + (5 + 6y² - 8xy + x²) + Side C

→ (7x² - 17xy + 5y² + 8) = (4x² + x² - 7xy - 8xy + 4y² + 6y² - 3 + 5) + Side C

→ (7x² - 17xy + 5y² + 8) = (5x² - 15xy + 10y² + 2) + Side C

→ (7x² - 17xy + 5y² + 8) - (5x² - 15xy + 10y² + 2) = Side C

→ Side C = (7x² - 17xy + 5y² + 8) - 5x² + 15xy - 10y² - 2

→ Side C = 7x² - 5x² - 17xy + 15xy + 5y² - 10y² + 8 - 2

→ Side C = 2x² - 2xy - 5y² + 6

The third side of the triangle is 2x² - 2xy - 5y² + 6.