Question

16. The perimeter of a triangle is 15xsquare - 23x +9 and two of its sides
are 5xsquare +8x - 1 and 6xsquare - 9x +4. Find the third side.
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Answer 1

Answer:

The third side is 3x² - 22x + 6.

Step-by-step explanation:

Given :

Perimeter of the triangle = 15x² - 23x + 9

One side = 5x² + 8x - 1

Second side = 6x² - 9x + 4

To find :

The third side

Solution :

Perimeter of triangle = Sum of all sides

$\sf{\longrightarrow} \: 15 {x}^{2} - 23x + 9 = 5 {x}^{2} + 8x - 1 + (6 {x}^{2} - 9x + 4) + (Side \: 3) \\ \\ \sf{\longrightarrow} \: 15 {x}^{2} - 23x + 9 =(5 {x}^{2} + 6 {x}^{2} + 8x - 9x - 1 + 4) + (Side \: 3) \\ \\ \sf{\longrightarrow} \: 15 {x}^{2} - 23x + 9 =11 {x}^{2} - x + 3 + (Side \: 3) \\ \\ \sf{\longrightarrow} \: Side \: 3 = 15 {x}^{2} - 23x + 9 - (11 {x}^{2} - x + 3 ) \\ \\ \sf{\longrightarrow} \: Side \: 3 = 15 {x}^{2} - 23x + 9 -11 {x}^{2} + x - 3 \\ \\ \sf{\longrightarrow} \: Side \: 3 = 15 {x}^{2} - 11 {x}^{2} - 23x + x + 9 - 3 \\ \\ \sf{\longrightarrow}\red{ \: Side \: 3 = 3 {x}^{2} - 22x + 6}$

Third Side = 3x² - 22x + 6

$\therefore$ The third side is 3x² - 22x + 6.

Answer 2

Given,

Perimeter of triangle = $15x^{2}-23x+9$

First side of triangle = $5x^{2}+8x-1$

Second side of triangle = $6x^2-9x+4$

Unknown side = Third side

We know,

Perimeter of triangle = Sum of all sides of triangle

$15x^{2}-23x+9=(5x^{2}+8x-1)+(6x^{2}-9x+4)+(ThirdSide)\\\\15x^{2}-23x+9=11x^2-x+3+(ThirdSide)\\\\3x^2-22x+6=(ThirdSide)$

Value of third Side = $3x^2-22x+6$