Question

The longest side of a triangle is 4 inches longer than the shortest side. The medium side is 3 inches longer than the shortest side. If the perimeter of the triangle is 25 inches, what are the lengths of the 3 sides

Answer 1

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