Problema Solution

a triangle has a perimeter of 13. the two shorter sides have integer lengths equal to x and x+ 1. what could be the lengths of the three sides of the triangle ?

Answer provided by our tutors

let 'y' be the length of the third side


x + x + 1 + y = 13


2x +1 + y = 13


and


x < y


x + 1 < y


2x + 1 < 2y


2x + 1 + y < 3y


13 < 3y


13/3 < y


for y = 5 we have


2x + 1 + 5 = 13


2x + 1 = 7


x = 3.5


but we need x to be integer thus we try for the next value for y


for y = 6 we have


2x + 1 + 6 = 13


x = 3


x + 1 = 3 +1 = 4


we found one possible solution for the sides of the triangle: 3, 4 and 6.