the perimeter of a triangle is 7x sq-17xy+5y sq+8 and two of its sides are 4x sq-7xy+4y sq-3 and 5+6y sq - 8xy +x .find the third side of the triangle
Answer :
Given : Perimeter of triangle = 7 x 2 - 17 xy + 5 y 2 + 8
And
Length of two sides are 4 x 2 -7 xy + 4 y 2 - 3 and 5 + 6 y 2 - 8 xy + x
Let length of third side = l
We know perimeter of triangle = Sum of all three sides ,So
4 x 2 -7 xy + 4 y 2 - 3 + 5 + 6 y 2 - 8 xy + x + l = 7 x 2 - 17 xy + 5 y 2 + 8
4 x 2 -15 xy + 10 y 2 + 2 + x + l = 7 x 2 - 17 xy + 5 y 2 + 8
l = 7 x 2 - 17 xy + 5 y 2 + 8 - ( 4 x 2 -15 xy + 10 y 2 + 2 + x )
l = 7 x 2 - 17 xy + 5 y 2 + 8 - 4 x 2 +15 xy - 10 y 2 - 2 - x
l = 3 x 2 - 2 xy - 5 y 2 + 6 - x
So,
Length of third side = 3 x 2 - 2 xy - 5 y 2 + 6 - x ( Ans )
Given : Perimeter of triangle = 7 x 2 - 17 xy + 5 y 2 + 8
And
Length of two sides are 4 x 2 -7 xy + 4 y 2 - 3 and 5 + 6 y 2 - 8 xy + x
Let length of third side = l
We know perimeter of triangle = Sum of all three sides ,So
4 x 2 -7 xy + 4 y 2 - 3 + 5 + 6 y 2 - 8 xy + x + l = 7 x 2 - 17 xy + 5 y 2 + 8
4 x 2 -15 xy + 10 y 2 + 2 + x + l = 7 x 2 - 17 xy + 5 y 2 + 8
l = 7 x 2 - 17 xy + 5 y 2 + 8 - ( 4 x 2 -15 xy + 10 y 2 + 2 + x )
l = 7 x 2 - 17 xy + 5 y 2 + 8 - 4 x 2 +15 xy - 10 y 2 - 2 - x
l = 3 x 2 - 2 xy - 5 y 2 + 6 - x
So,
Length of third side = 3 x 2 - 2 xy - 5 y 2 + 6 - x ( Ans )