Question

perimeter of triangle is 9x²-16 x+1 and two of its sides are 2x²+6x-4 and 9x²-11 x+1 find the third side
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Answer 1

Step-by-step explanation:

perimeter of triangle = side + side + side

9x² -6x +1 = 2x² + 6x-4 + 9x²-11x + 1

after adding rhs which are the given sign we get 11x² -5x -3. then subtract the sum of sides from perimeter .

we get -2x² -11x +4

Answer 2

Given:

• Perimeter of the triangle.
• Two sides of the triangle.

To find:

• The third side.

Solution:

Perimeter of triangle=9x²-16x+1

First side of the triangle=2x²+6x-4

Second side of the triangle=9x²-11 x+1

We know that.

$\sf\fbox\pink{Perimeter\:of\:∆=Sum\:of\:all\:sides}$

$\longrightarrow$$9x²-16x+1=(2x²+6x-4)+(9x²-11 x+1)+Side3$

$\longrightarrow$$9x²-16x+1=2x²+9x²+6x-11x-4+1+Side3$

$\longrightarrow$$9x²-16x+1=11x²-5x-3+Side3$

$\longrightarrow$$9x²-16x+1=11x²-5x-3+Side3$

$\longrightarrow$$9x²-11x²-16x+1=5x-3+Side3$

$\longrightarrow$$-2x²-16x+5x+1+3=Side3$

$\longrightarrow$$-2x²-11x+4=Side3$

$\longrightarrow$ $Side3= -2x²-11x+4$

Therefore,the third side of the triangle is $-2x²-11x+4.$

$\sf\fbox\green{Verification:}$

$\implies(2x²+6x-4)+(9x²-11 x+1)+(-2x²-11x+4)=9x²-16 x+1$

$\implies2x²+9x²-2x²+6x-11x-11x-4+1+4=9x²-16 x+1$

$\implies11x²-2x²-5x-11x-3+4=9x²-16 x+1$

$\implies9x²-16x+1=9x²-16 x+1$

Hence, Verified.