# 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.