Question

1.The sides of a triangle are x - 3xy + 8,
4x2 + 5xy - 3 and 6 - 3x2 + 4xy.
Find its perimeter.

2.The perimeter of a triangle is 8y2 – 9y + 4 andits two sides are 3y2 - 5y and 4y2 +12
Find its third side.​

Answer 1

Step-by-step explanation:

1. Required perimeter = Sum of three sides.

= x2 – 3xy + 8 + 4x2 + 5xy – 3 + 6 – 3x2 + 4xy.

= x2 + 4x2 – 3x2 – 3xy + 5xy + 4xy + 8 – 3 + 6.

= 2x2 + 6xy + 11.

2. Perimeter of the triangle = Sum of three sides

= 8y2 – 9y + 4

Sum of two sides = 3y2 – 5y + 4y2 + 12

= 7y2 – 5y + 12

∴ (8y2 – 9y + 4) – (7y2 – 5y + 12)

= 8y2 – 9y + 4 – 7y2 + 5y – 12

= y2 – 4y – 8

Hence third side = y2 – 4y - 8