Posted by tee on Monday, November 4, 2013 at 1:20am.
a = the length of the shortest side
b = the length of the middle side
c = the length of the longest side
P = the perimeter
The perimeter of a triangle is 42 inches.
P = a + b + c
a + b + c = 42 Subtract c to both sides
a + b + c - c = 42 - c
a + b = 42 - c
The sum of the length of the longest side and twice the sum of both the other side lengths is 65 inches.
c + 2 ( a + b ) = 65
c + 2 ( 42 - c ) = 65
c + 2 * 42 - 2 * c = 65
c + 84 - 2 c = 65
- c + 84 = 65 Add c to both sides
- c + 84 + c = 65 + c
84 = 65 + c Subtract 65 to both sides
84 - 65 = 65 + c - c
19 = c
c = 19 in
Three times the length of the longest side minus the length of the shortest side is 49 inches.
3 c - a = 49 Add a to both sides
3 c - a + a = 49 + a
3 c = 49 + a Subtract 49 to both sides
3 c - 49 = 49 + a - 49
3 c - 49 = a
a = 3 c - 49
a = 3 * 19 - 49
a = 57 - 49 = 8
a = 8 in
a + b + c = 42
8 + b + 19 = 42
27 + b = 42 Subtract 27 to both sides
27 + b - 27 = 42 - 27
b = 15 in
The side lengths:
a = 8 in
b = 15 in
c = 19 in
84 = 65 + c Subtract 65 to both sides
84 - 65 = 65 + c - 65
19 = c
c = 19 in