SOLUTION: The lengths of the sides of a triangle in inches are three consecutive integers. The length of the shortest side is 25% of the perimeter. What is the length of the longest side?

Algebra ->  Expressions-with-variables -> SOLUTION: The lengths of the sides of a triangle in inches are three consecutive integers. The length of the shortest side is 25% of the perimeter. What is the length of the longest side?      Log On


   

Question 1183406: The lengths of the sides of a triangle in inches are three consecutive integers. The length of the shortest side is 25% of the perimeter. What is the length of the longest side?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The lengths of the sides of a triangle in inches are three consecutive integers.
The length of the shortest side is 25% of the perimeter.
What is the length of the longest side?
~~~~~~~~~~~~~~~~~~ 

Let the side lengths be  (n-1), n and (n+1)  inches.


Then the perimeter is  (n-1) + n + (n+1) = 3n  inches.


From the description, we have this equation


    n-1 = %281%2F4%29%2A%283n%29  inches.


Multiply both sides by 4, simplify and solve


    4n - 4 = 3n

    4n - 3n = 4

       n    = 4.


The triangle sides are of the length 3, 4 and 5 inches.      

The longest side is 5 inches.                              ANSWER

Solved.

It is a classic (3,4,5) right angled triangle.


Happy learning (!)