Question

In triangle ABC, side AB is one-third of the length of side AC. Side BC is 5 more than the length of side AC. The perimeter is 19. What is the length of side AC?

Answer 1

• AC = 6 units

===========

Given

• AB = AC/3
• BC = AC + 5
• P = 19
• AC = ?

Solution

• P = AB + AC + BC

Substitute and solve for AC

• AC/3 + AC + AC + 5 = 19
• 2 1/3 AC = 14
• 7/3 AC = 14
• AC = 14*3/7
• AC = 6

Note:

Other sides are 2 and 11. This is not a correct question as sum of two smaller sides (2 + 6) is less than the longest one (11), hence there is no such possible triangle.