Question 658963
Let c = the longest side
Let a = one side
Let b = the other side
The perimeter, p, is given by
(1) p = a + b + c
From the problem statement we have
(2) a = c/2 and
(3) b = c - 12
Substitute (2) and (3) into (1) and get
(4) p = c/2 + c - 12 + c or
(5) p = (5/2)c - 12
Using the given value of p yields
(6) (5/2)c - 12 = 53 or
(7) (5/2)c = 65 or
(8) 5c = 130 or
(9) c = 26
Then
a = 13 and b = 14.
Let's check these values.
Is (26+13+14 = 53)?
Is (53 = 53)? Yes
Answer: The three sides of the triangle are 26, 13 and 14 units in lenght.