Question 386801
Let a be the length of the shortest side 
Let b be the length of the mid-length side
Let c be the length of the longest side

These form a perimeter of 59 cm, so:
1. a + b + c = 59


The longest side is 7 cm less then the sum of the other two sides. So:
2. c = a + b - 7


Twice the shortest side is 10 cm less than the longest side. So:
3. 2*a = c - 10


First, substitute the value of c from eq 2 into eq 1:
a + b + c = 59
a + b + (a + b - 7) = 59
2*a + 2*b - 7 = 59
Add 7 to both sides:
2a + 2b - 7 + 7 = 59 + 7
4. 2a + 2b = 66


Now substitute the value of c from eq 2 into eq 3:
2*a = c - 10
2a = (a + b - 7) - 10
2a = a + b -17
Subtract a from both sides:
2a - a = a + b - 17 - a
5. a = b - 17


Now plug the expression for a in eq 5 back into eq 4:
2a + 2b = 66
2(b - 17) + 2b = 66
Distribute the 2:
2b - 17*2 + 2b = 66
2b - 34 + 2b = 66
Combine the b terms:
4b - 34 = 66 
Add 34 to both sides to isolate the term with the variable (b):
4b - 34 + 34 = 66 + 34
4b = 100
Divide both sides by 4 to solve for b:
(4b)/4 = 100/4
b = 25


Now use eq 5 to solve for a:
a = b - 17
a = 25 - 17
a = 8


Now use eq 2 to solve for c:
c = a + b - 7
c = 8 + 25 - 7
c = 26