Question

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

Answer 1

Perimeter of the triangle = 6p² – 4p + 9

Two sides are;

Side one = p² – 2p + 1 and

Side two = 3p² – 5p + 3

Let’s take third side be = x

As we know perimeter of a triangle = sum of all the sides

So, we have

6p² – 4p + 9 = {(p² – 2p + 1) + (3p² – 5p + 3) + (x)}

6p² – 4p + 9 = p² – 2p + 1 + 3p² – 5p + 3 + x

6p² – 4p + 9 - p² + 2p – 1 - 3p² + 5p - 3 = x

Let’s make the pairs;

(6p² – p² – 3p²) + (- 4p + 2p + 5p) + (9 – 1 – 3) = x

2p² + 3p + 5 = x

The required side is 2p² + 3p + 5.