Answer:
Longest side = 10 inches
Medium side = 9 inches
Shortest side = 6 inches
Explanation:
Let the longest side be L, the medium side be M and the shortest side be S
From the data,
L = S + 4
(The longest side of a triangle is 4 inches longer than the shortest side)
M = S + 3
(The medium side is 3 inches longer than the shortest side)
Perimeter of the triangle
P = L + M + S
Substituting for L and M in terms of S:
P = (S + 4) + (S + 3) + S
P = S + S + S + 4 + 3
P = 3S + 7
We are given that perimeter P = 25 inches
So,
3S + 7 = 25
Subtract 7 from both sides
3S = 25-7 = 18
Divide by 3 both sides:
3S/3 = 18/3
S = 6
So shortest side is 6 inches
Longest side L = 6 + 4 = 10 inches
Medium side M = 6 + 3 = 9 inches