The perimeter of a triangle is 43 feet.The small side is three was in the middle side, and the largest size to less than twice the middle side. What is the length of the longest side?

the perimiter of the triangle at the right is 43 cm. find the length of the side marked with an x

To solve this problem, we first need to understand the relationships between the sides of the triangle.

Let's assume that the small side of the triangle has a length of x feet. Since the middle side is three times the small side, the middle side would be 3x feet. Similarly, the largest side is less than twice the middle side, so the largest side would be less than 2 * 3x = 6x feet.

Now, let's use the information given to form an equation for the perimeter of the triangle:

Perimeter = Small Side + Middle Side + Largest Side

Substituting the given values:

43 = x + 3x + (less than 6x)

To find the length of the longest side, we need to determine the maximum value of the largest side, which occurs when it is equal to 6x. However, we also need it to be less than 6x since it is mentioned to be less than twice the middle side.

Hence, we can rewrite the equation:

43 = x + 3x + 6x (since this is the maximum value for the largest side)

Simplifying the equation:

43 = 10x

Now, divide both sides by 10:

43/10 = x

So, x ≈ 4.3 feet.

Therefore, the length of the longest side is less than twice the middle side, which is less than 2 * 3(4.3) = 25.8 feet.

Please proofread and clarify.

small side is three was in the middle side

largest size to less than twice