Question

the perimeter of a triangle is 6p²-4p+9and two of its sides are p²-2p+1 and 3p²-5p+3. find the third side of the triangle

Answer 1

$\mathbf{Perimeter \: \: of \: \: triangle = sum \: \: of \: \: a ll \: \: three \: \: sides}$



According to the question,


6p² - 4p + 9 = p² - 2p + 1 + 3p² - 5p + 3 + third side



=> 6p² - 4p + 9 = p² + 3p² - 2p - 5p + 1 + 3 + third side



=> 6p² - 4p + 9 = 4p² - 7p + 4 + third side


=> 6p² - 4p² - 4p + 7p + 9 - 4 = third side



=> 2p² + 3p + 5 = third side

Answer 2

Hello dear,

Here is your answer,

Given :-
Perimeter of triangle is (6p² - 4p + 9)
Two sides are,
(p² - 2p + 1) and (3p² - 5p + 3)

We know that,
Perimeter of triangle = sum of all sides

So,

(p² - 2p + 1) + (3p² - 5p + 3) + third side = (6p² - 4p + 9)

=> p² - 2p + 1 + 3p² - 5p + 3 + third side = (6p² - 4p + 9)

=> 4p² - 7p + 4 + third side = (6p² - 4p + 9)

=> third side = (6p² - 4p + 9) - (4p² - 7p + 4)

=>third side = (6p² - 4p + 9 - 4p² + 7p - 4)

=> third side = 2p² + 3p + 5


Check :

One side = (p² - 2p + 1)
second side = (3p² - 5p + 3)
third side = (2p² + 3p + 5)

So, sum of all three sides =

..( p² - 2p + 1)
+(3p² - 5p + 3)
+(2p² + 3p + 5)
————————
(6p² - 4p + 9)


Hope it helps.