One side of the triangle is 1 cm shorter than the second side and 1 cm longer than the third side.
| February 13, 2021 | education
One side of the triangle is 1 cm shorter than the second side and 1 cm longer than the third side. Find the larger side of the triangle if its perimeter is 12 cm.
Let we have a triangle ABC, the sides of which are AB, BC, AC, while BC = AB – 1, AC = AB + 1. The perimeter p = 12 cm, therefore, based on the conditions of the problem:
AB + BC + AC = 12,
AB + (AB – 1) + (AB + 1) = 12,
AB + AB – 1 + AB + 1 = 12,
3 * AB = 12,
AB = 4 cm,
BC = AB – 1 = 4 – 1 = 3 cm,
AC = AB + 1 = 4 + 1 = 5 cm.
The longest side of the triangle ABC is the side AC = 5 cm.
Answer: AC = 5 cm.
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