Question

The perimeter of a triangle is 14a² + 20a + 13. Two of its sides are 3a² + 5a + 1 and a² + 10a – 6. Find its third side. 

Answer 1

perimeter of a triangle = 14a² + 20a + 13

Sum of two sides

= 3a² + 5a + 1 + a² + 10a - 6

= 3a² + a² + 5a + 10a + 1 - 6

= 4a² + 15a - 5

∴ Third side = (14a² + 20a + 13) - (4a² + 15a - 5)

= 14a² + 20a + 13 - 4a² - 15a + 5

= 14a² - 4a² + 20a - 15a + 13 + 5 

= 10a² + 5a + 18