The perimeter of a triangle is 57in. The longest side is 13in. longer than the medium side, and the medium side is 7 in. more than the shortest side. find the length of each side of the triangle.

The length of the longest side is ___in, the length of the medium side is __in. and the length of the shortest side ___in.

x=17

x-7=10+17=27+17=44+13=57

Let's denote the length of the shortest side as "x" inches.

According to the information given, the medium side is 7 inches more than the shortest side, so its length would be x + 7 inches.

And the longest side is 13 inches longer than the medium side, so its length would be (x + 7) + 13 = x + 20 inches.

The perimeter of a triangle is the sum of the lengths of all three sides. Therefore, we can set up the following equation:

x + (x + 7) + (x + 20) = 57

Combining like terms, we simplify the equation:

3x + 27 = 57

Next, subtract 27 from both sides of the equation:

3x = 57 - 27

This simplifies to:

3x = 30

Finally, divide both sides of the equation by 3 to solve for x:

x = 30 / 3

Thus, the length of the shortest side is x = 10 inches.

The length of the medium side is x + 7 = 10 + 7 = 17 inches.

The length of the longest side is x + 20 = 10 + 20 = 30 inches.

Therefore, the length of each side of the triangle is as follows:

The length of the longest side is 30 inches.
The length of the medium side is 17 inches.
The length of the shortest side is 10 inches.

To find the lengths of each side of the triangle, let's assign variables to each side:

Let the shortest side be x inches.
The medium side is 7 inches longer, so it would be x + 7 inches.
The longest side is 13 inches longer than the medium side, so it would be x + 7 + 13 inches, which simplifies to x + 20 inches.

Now, let's set up the equation based on the perimeter of the triangle:

Perimeter = Sum of all sides
57 inches = x + (x + 7) + (x + 20)

To solve this equation, we can combine like terms:

57 inches = 3x + 27

Next, let's isolate the variable:

3x = 57 - 27
3x = 30

Now, divide both sides by 3 to solve for x:

x = 30 / 3
x = 10

So, the length of the shortest side is 10 inches.

Now we can substitute this value back into our expressions for the other sides:

Medium side length = x + 7 = 10 + 7 = 17 inches
Longest side length = x + 20 = 10 + 20 = 30 inches

Therefore, the length of the longest side is 30 inches, the length of the medium side is 17 inches, and the length of the shortest side is 10 inches.

well, just use what you're told. If the medium side is x, then

x-7 + x + x+13 = 57

Now just find x and you're almost done.