The length of the sides of a triangle are three consecutive even integers. The perimeter of the triangle is 36 in. What is the length of the longest side of the triangle?

let 3 sides be x, x+2, and x+4

x + x+2 + x+4 = 36
3x = 30
x = 10

sides are 10, 12 and 14

36/3 = 12

Try that plus the even numbers just below and just above 12.

Well, if the sides of the triangle are three consecutive even integers, we can represent them as x, x+2, and x+4.

Since the perimeter of the triangle is given as 36 in, we can set up the equation:

x + (x+2) + (x+4) = 36

Simplifying, we get:

3x + 6 = 36

Subtracting 6 from both sides gives us:

3x = 30

Dividing both sides by 3, we find:

x = 10

So, the three sides of the triangle are 10, 12, and 14.

Therefore, the longest side of the triangle is 14 inches. But hey, don't worry, it's still shorter than a giraffe's neck!

Let's solve this step-by-step:

Step 1: Let's represent the three consecutive even integers as x, x + 2, and x + 4 (since consecutive even integers have a difference of 2).

Step 2: According to the given information, the perimeter of the triangle is 36 inches. The perimeter of a triangle is the sum of the lengths of its sides.

So, we can write the equation: x + (x + 2) + (x + 4) = 36

Step 3: Simplify the equation:

3x + 6 = 36

Step 4: Subtract 6 from both sides of the equation:

3x = 30

Step 5: Divide both sides of the equation by 3:

x = 10

Step 6: Now, we know that x = 10. Let's substitute this value to find the lengths of the three sides:

The three consecutive even integers are:
x = 10
x + 2 = 10 + 2 = 12
x + 4 = 10 + 4 = 14

Step 7: Lastly, we need to determine the length of the longest side. The longest side corresponds to the largest of the three consecutive even integers, which is 14 inches.

So, the length of the longest side of the triangle is 14 inches.

To find the length of the longest side of the triangle, we first need to determine the three consecutive even integers that represent the lengths of the sides.

Let's use the variable "x" to represent the first even integer. Since the sides are consecutive even integers, the second side would be "x + 2", and the third side would be "x + 4".

The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is given as 36 inches.

So, we can set up the following equation, using the values we have determined:

x + (x + 2) + (x + 4) = 36

Now, we can solve this equation to find the value of x, which represents the length of the first side of the triangle.

Combining like terms:

3x + 6 = 36

Subtracting 6 from both sides:

3x = 30

Dividing both sides by 3:

x = 10

Now that we have found the value of x, we can substitute it back into our expressions for the second and third sides of the triangle:

Second side = x + 2 = 10 + 2 = 12
Third side = x + 4 = 10 + 4 = 14

Therefore, the lengths of the sides of the triangle are 10 inches, 12 inches, and 14 inches. The longest side is 14 inches.