The perimeter of a triangle is 20 inches. The longest side is 4 inches longer than the shortest side, and the shortest side is three -fourths the length of the middle side. Find the length of each side of the triangle

Two side triangle have the same lenght. The third side measures 5 m less than twice the common lenght. The perimeter of the triange is 23 m. What are the lenghts of the three sides?

a triangle has a permeter of 23 inches. the meduim side is 3 inches more then the shortest side, and the longest side is twice the shortest side. find the shortest side.

To find the length of each side of the triangle, we can set up a system of equations based on the given information.

Let's denote the lengths of the sides as follows:
- Shortest side: x inches
- Middle side: y inches
- Longest side: z inches

Based on the given information:
1) The longest side is 4 inches longer than the shortest side:
z = x + 4

2) The shortest side is three-fourths the length of the middle side:
x = (3/4)y

3) The perimeter of the triangle is 20 inches:
x + y + z = 20

Now, we can substitute the values from equations 1 and 2 into equation 3 and solve for x, y, and z.

Substituting z = x + 4 and x = (3/4)y into x + y + z = 20:
(3/4)y + y + (3/4)y + 4 = 20

Combining like terms:
(11/4)y + 4 = 20

Subtracting 4 from both sides:
(11/4)y = 16

Multiplying both sides by 4/11 to isolate y:
y = (16 * 4) / 11
y = 64 / 11
y ≈ 5.818 (rounded to 3 decimal places)

Substituting y ≈ 5.818 into x = (3/4)y:
x = (3/4)(5.818)
x ≈ 4.364 (rounded to 3 decimal places)

Substituting x ≈ 4.364 into z = x + 4:
z = 4.364 + 4
z ≈ 8.364 (rounded to 3 decimal places)

Therefore, the lengths of the sides of the triangle are approximately:
Shortest side: x ≈ 4.364 inches
Middle side: y ≈ 5.818 inches
Longest side: z ≈ 8.364 inches

Let x = shortest side, then x + 4 = longest and middle = 4/3x

x = 3/4m ---> 4/3x = m

x + x + 4 + 4/3x = 20

Solve for x and then the other sides.