Question

The perimeter of a triangle is 7p^2-8p+9 and two of its sides are 2p^2-p+1 and 11p^2-3p+5.find the third side of the triangle.

Answer 1

To Find :

• we need to find the third side of triangle.

$\large\underline{ \underline { \boldsymbol{Solution : - }}}$

• Perimeter of triangle = 7p² - 8p + 9
• Given two sides are :-
• 2p² - p + 1 and 11p² - 3p + 5

$\text{Let the third side of triangle be x}$

As we know that,

$\text{Perimeter of triangle =sum \: of \: all \: sides }$

So,

››➔ x + (2p² - p + 1) + (11p² - 3p + 5) = 7p² - 8p + 9

››➔ x + 2p² - p + 1 + 11p² - 3p + 5 = 7p² - 8p + 9

››➔ x +13p² - 4p + 6 = 7p² - 8p + 9

››➔ x = 7p² - 8p + 9 -(13p² - 4p + 6)

››➔ x = 7p² - 8p + 9 - 13p² + 4p - 6

››➔ x = - 6p² - 4p + 3

Hence,

• The third side is - 6p² - 4p + 3.

♻️Verification : -

Perimeter of triangle = 7p² - 8p + 9

›› (2p² - p + 1) + (11p² - 3p + 5) + (-6p² - 4p + 3) = 7p² - 8p + 9

›› 2p² - p + 1 + 11p² - 3p + 5 - 6p² - 4p + 3 = 7p² - 8p + 9

›› 13p² - 6p² - 4p - 4p + 6 + 3 = 7p² - 8p + 9

›› 7p² - 8p + 9 = 7p² - 8p + 9

LHS = RHS

Hence Verified

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Answer 2

$\bf{\underline{Question:-}}$

The perimeter of a triangle is 7p²-8p+9 and two of its sides are 2p²-p+1 and 11p²-3p+5.find the third side of the triangle.

$\bf{\underline{Given:-}}$

• Perimeter of ∆ 7p²-8p+9
• $\sf side_1 = 2p^2-p+1$
• $\sf Side_2 =11p^2-3p+5$

Perimeter of ∆ = Sum of all sides

$\sf$$\sf$OR$\sf$$\sf$

† Perimeter = $\bf Side_1 + Side_2 + Side_3$

$\rm→7p^2 - 8p+9 = 2p^2-p+1+11p^2-3p+5+Side_3$

$\rm→7p^2 - 8p+9 = 13p^2-4p+6+Side_3$

$\rm Side_3 = -7p^2+8p-9+2p^2-p+1+11p^2-3p+5$

$\sf Side_3=-7p^2+8p-8+13p^3-4p+6$

$\rm Side_3 = -6p^2-4p+3$

$\bf{\underline{Hence:-}}$

• Third side is -6p² -4p + 3