Find the perimeter using substitution for the system of equations.

Question

The perimeter of a triangle is 24 inches. The longest side is 4 inches longer the the shortest side, and the shortest side is three-fourths the length of the middle side. Find the length of each side using substitution.

Answer 1

using only one variable if this is easier...

middle side=m

shortest side=0.75m

longest side=0.75m+4

24=m+0.75m+0.75m+4

24=2.5m+4

24-4=2.5m

20=2.5m

200=25m

m=200/25

m=8 inches

middle side=8 inches

shortest side=0.75*8=6 inches

longest side=0.75*8+4=6+4=10 inches

Answer 2

Hi Linda, the perimeter of a triangle is the sum of the sides. Let L represent the longer side, S the shorter side, and M the middle length side.

 

Then, L + S + M = P

 

Given:

 

P = 24 inches

 

S = L - 4, the shortest side is equal to the longest side - 4 inches.

 

S = 3 / 4 * M, or the shortest side is equal to three-fourths of the middle side.

 

Replace S and M in the perimeter equation:

 

S = L - 4, and S = 3 /4 * M

 

Find M in terms of L, or L - 4 = 3 / 4 * M.

 

M = (4L - 16) / 3.

 

Substitute:

 

L + L - 4 + (4L - 16) / 3 = 24

 

Clear the fraction:

 

3L + 3L - 12 + 4L - 16 = 72

 

10L - 28 = 72

 

Add 28 to both sides:

 

10L = 100

 

Divide both sides by 10:

 

L = 10

 

The longest side is 10 inches.

 

The shortest side is L - 4, or 6 inches.

 

The Middle side is 4 / 3 * S, or 8 inches.

 

10 + 6 + 8 = 24.

 

Questions?