Question

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

Answer 1

Answer:

2p² + 3p + 5

Step-by-step explanation:

Given perimeter of a triangular field = 6p² - 4p  + 9.

Given,1st side = p² - 2p + 1

Given,2nd side = 3p² - 5p + 3.

We know that perimeter = Sum of all three sides.

⇒ 6p² - 4p + 9 = p² - 2p + 1 + 3p² - 5p + 3 + S

⇒ 6p² - 4p + 9 = 4p² - 7p + 4 + S

⇒ 6p² - 4p + 9 - 4p² + 7p - 4 = S

⇒ 2p² + 3p + 5 = S.

Therefore,the third Side = 2p² + 3p + 5.

Hope it helps!

Answer 2

perimeter of triangle is always equals to the sum of all it's side i.e. side AB=c BC=a CA=b then perimeter= a+b+c
here side a + side b + side c = 6p² - 4p + 9
(p² - 2p + 1 ) + (3p² - 5p + 3) + side c= 6p²-4p+9
(4p²-7p+4) + side c = 6p²-4p+9
side c = (6p²-4p+9) - (4p²-7p+4)
side c = 2p²+3p+5
the third side is equals to 2p²+3p+5