Question

The perimeter of a triangle is 7 2 − 8 + 9 and two of its sides are 2 2 − + 1 and 11 2 − 3 + 5. Find the expression for the length of the third side of the triangle.​

Answer 1

Answer:

Perimeter of a triangle = 7p

2

−5p+11

And, two of its sides are p

2

+2p−1 and 3p

2

−6p+3

We know that,

Perimeter of a triangle = Sum of three sides of triangle

⇒ 7p

2

−5p+11=(p

2

+2p−1)+(3p

2

−6p+3)+( Third side of triangle) 7p

2

−5p+11=(4p

2

−4p+2)+( Third side of triangle)

⇒ Third side of triangle=(7p

2

−5p+11)−(4p

2

−4p+2)

= (7p

2

−4p

2

)+(−5p+4p)+(11−2)

= 3p

2

−p+9

Thus, the third side of the triangle is 3p

2

−p+9.