Answer:
14 cm, 27 cm, 33 cm
Step-by-step explanation:
You want the three sides of a triangle such that their sum is 74 cm, the longest is 8 cm less than the sum of the other two, and twice the shortest is 5 cm less than the longest.
Let a, b, c represent the lengths of the sides in order from shortest to longest. The given relations are ...
a + b + c = 74
c = a + b -8
2a = c - 5
Adding 8 to the second equation and using that to substitute for (a+b) in the first, we have ...
c +8 = a +b
(c +8) +c = 74
2c = 66 . . . . . . . . . subtract 8
c = 33 . . . . . . . . . . divide by 2
Using this in the third equation, we have ...
2a = 33 -5
a = 28/2 = 14 . . . . . . divide by 2
Either of the first two equations can be used to find b.
14 +b +33 = 74
b = 74 -47 = 27
The lengths of the sides of the triangle are 14 cm, 27 cm, and 33 cm.