what's the shortest side medium side and longest side

Question

The longest side of a triangle is

5

inches longer than the shortest side. The medium side is

4

inches longer than the shortest side. If the perimeter of the triangle is

30

​inches, what are the lengths of the three​ sides?

Answer 1

Let L = the length of longest side

Let S = the length of shortest side

Let M = the length of the medium side

From the problem we have:

L = 5 + S (i)

M = 4 + S (ii)

S + M + L = 30 (iii)

Substituting (i) and (ii) into (iii) we get:

S + M + L = 30

S + (4 + S) + (5 + S) = 30

Gathering like terms we get:

(S + S + S) + (4 + 5) = 30

3S + 9 = 30

Solving for S by moving 9 to the right side by adding (-9) to each side of the equation we get :

(-9) + 3S +9 = 30 + (-9)

3S = 21

Multiply both sides of the equation by 1/3 to solve for the shortest side:

(1/3) 3S = 21 (1/3)

S = 7

Plugging back into (i) to find the length of the longest side:

L = 5 + S

L = 5 + 7

L = 12

Plugging back into (ii) to find the length of the medium side:

M = 4 + S 

M = 4 + 7

M = 11

Checking our work with (iii):

S+ M + L = 30

7 + 11 + 12 = 30

30 = 30

Hope this is helpful!

Answer 2

Let x = length of the shortest side

x + 5 = length of longest side

x + 4 = length of the remaining side

x + (x + 5) + (x + 4) = 30

Solve for x.