Problema Solution
The perimeter of a triangle is 45 centimeters. The longest side is 3 centimeter(s) less than the sum of the other two sides. Twice the shortest side is 11 centimeters less than the longest side. Find the lengths of each side of the triangle
Answer provided by our tutors
let the sides of the triangle be 'a', 'b' and 'c' and we can assume, without losing generality, that a<b<c
the perimeter of a triangle is 45 centimeters
a + b + c = 45
the longest side is 3 centimeter(s) less than the sum of the other two sides
c = a + b - 3
twice the shortest side is 11 centimeters less than the longest side
2a = c - 11
by solving the system of equations
2a = c - 11
c = a + b - 3
a + b + c = 45
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we find
a = 5 cm
b = 19 cm
c = 21 cm
the lengths of the sides of the triangle are 5 cm, 19 cm and 21 cm.