.The first side of a triangle is twice as long as the second side and the third side is 5 more than the first side. If the perimeter of the triangle is 65 cm. Which of the following is the smallest side?

let the 2nd side be x

then the first side is 2x
and the third side is 2x+5
( I just translated all the English into Math)

Perimeter is the sum of all the sides, so
x + 2x + 2x+5 = 65
5x = 60
x = 12

sides are 24, 12, 29

Well, when it comes to triangles, size does matter! Let's break it down. Let's call the second side x. According to the question, the first side is twice as long, so it would be 2x. The third side is 5 more than the first side, which means it would be 2x + 5.

Now, we know that the perimeter of a triangle is the sum of all three sides. So, we can set up an equation: x + 2x + (2x + 5) = 65. Let's solve this mathematical puzzle!

Combining like terms, we get 5x + 5 = 65. Subtracting 5 from both sides gives us 5x = 60. Finally, dividing both sides by 5 gives us x = 12.

So, the second side is 12 cm.

But wait, you asked for the smallest side! That would be x, which is 12 cm.

So, the smallest side of the triangle is 12 cm.

Let's denote the second side of the triangle as x cm. Now, according to the given information, the first side is twice as long as the second side, so it would be 2x cm. The third side is 5 more than the first side, so it would be 2x + 5 cm.

Now, we can calculate the perimeter of the triangle by summing up the lengths of all three sides:

Perimeter = First Side + Second Side + Third Side
65 = 2x + x + (2x + 5)

Simplifying the equation, we get:
65 = 5x + 5

Subtracting 5 from both sides, we have:
60 = 5x

Dividing both sides by 5, we find:
x = 12

Therefore, the second side of the triangle is 12 cm.

To find the smallest side, we can compare the lengths of all three sides:

First side = 2x = 2*12 = 24 cm
Second side = x = 12 cm
Third side = 2x + 5 = 2*12 + 5 = 24 + 5 = 29 cm

Therefore, the smallest side of the triangle is the second side, which is 12 cm.

To solve this problem, we need to set up an equation based on the given information and then solve for the lengths of the sides of the triangle.

Let's assume that the length of the second side of the triangle is x cm. According to the given information, the first side is twice as long as the second side, so the length of the first side is 2x cm. The third side is 5 more than the first side, so the length of the third side is (2x + 5) cm.

The perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation as follows:

2x + x + (2x + 5) = 65 cm

Now let's simplify and solve for x:

5x + 5 = 65

Subtracting 5 from both sides:

5x = 60

Dividing both sides by 5:

x = 12

Now we can substitute the value of x back into the equation to find the lengths of the sides:

First side = 2x = 2 * 12 = 24 cm

Second side = x = 12 cm

Third side = 2x + 5 = 2 * 12 + 5 = 29 cm

Now we can determine which side is the smallest. In this case, the second side is the smallest, with a length of 12 cm.

So the answer is: The smallest side of the triangle is 12 cm.