Answer:
The answer to your question is L = 10 in , M = 9 in ; S = 5 in
Step-by-step explanation:
Data
longest side = 5 + x in
medium side = 4 + x in
shortest side = x
Perimeter = 24 in
Process
1.- Write and equation to solve this problem
Perimeter = longest side + medium side + shortest side
Substitution
24 = (5 + x) + (4 + x) + x
Simplification
24 = 5 + x + 4 + x + x
24 = 9 + 3x
24 - 9 = 3x
15 = 3x
x = 15/3
x = 5
2.- Calculate the lengths of the side
Longest side = 5 + 5 = 10 in
Medium side = 5 + 4 = 9 in
Shortest side = 5 in
Answer: the shortest side is 5 inches.
The medium side is 9 inches.
The longest side is 10 inches
Step-by-step explanation:
Let x represent the length of the shortest side.
Let y represent the length of the medium side.
Let z represent the length of the longest side.
The longest side of a triangle is 5 inches longer than the shortest side. This means that
z = x + 5
The medium side is 4 inches longer than the shortest side. This means that
y = x + 4
If the perimeter of the triangle is 24 inches, it means that
x + y + z = 24 - - - - - - - - - - - - - -1
Substituting z = x + 5 and y = x + 4 into equation 1, it becomes
x + x + 4 + x + 5 = 24
3x + 9 = 24
3x = 24 - 9 = 15
x = 15/3 = 5
y = x + 4 = 5 + 4
y = 9
z = x + 5 = 5 + 5
z = 10
