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.