A flower bed is in the shape of a triangle with one side twice the length of the shortest​ side, and the third side is

30
feet more than the length of the shortest side. Find the dimensions if the perimeter is
138
feet

Well, let's call the length of the shortest side x. According to the problem, one side is twice the length of the shortest side, so that would be 2x. And the third side is 30 feet more than the length of the shortest side, so that would be x + 30.

To find the perimeter, we need to add up all the sides of the triangle: x + 2x + (x + 30).

Now we can set up an equation: x + 2x + (x + 30) = 138.

If we simplify the equation, we get 4x + 30 = 138. Subtracting 30 from both sides gives us 4x = 108.

Finally, dividing both sides by 4, we find that x = 27.

So, the length of the shortest side is 27 feet. The second side is 2 times that, so 2 * 27 = 54 feet. And the third side is 27 + 30 = 57 feet.

Therefore, the dimensions of the flower bed are 27 feet, 54 feet, and 57 feet.

Let's assume the length of the shortest side is x feet.

According to the problem, the second side is twice the length of the shortest side, so it is 2x feet.

The third side is 30 feet more than the length of the shortest side, so it is x + 30 feet.

To find the perimeter, we need to add all three sides together: x + 2x + (x + 30).

Since the perimeter is given as 138 feet, we can set up the equation as follows:
x + 2x + (x + 30) = 138.

Now, let's solve for x.

Combining like terms, the equation becomes:
4x + 30 = 138.

Next, we'll subtract 30 from both sides of the equation:
4x = 138 - 30,
4x = 108.

Finally, we'll divide both sides by 4 to solve for x:
x = 108 / 4,
x = 27.

Therefore, the shortest side of the triangle is 27 feet.

To find the dimensions of the other two sides, we'll substitute the value of x into the equations we derived earlier:

The second side = 2x = 2 * 27 = 54 feet.
The third side = x + 30 = 27 + 30 = 57 feet.

So, the dimensions of the triangle are: 27 feet, 54 feet, and 57 feet.

To solve this problem, let's first assign variables to the lengths of the sides of the triangle.

Let's call the length of the shortest side "x".
The length of the second side (twice the length of the shortest side) will be "2x".
The length of the third side (30 feet more than the shortest side) will be "x + 30".

We know that the perimeter of a triangle is calculated by adding the lengths of all three sides, so we can set up an equation:

Perimeter = x + 2x + (x + 30)

Given that the perimeter is 138 feet, we can write the equation as:

138 = x + 2x + (x + 30)

Now we can solve for x:

138 = 4x + 30
108 = 4x
x = 27

So the shortest side of the triangle is 27 feet.

Now we can find the lengths of the other sides:
Second side: 2x = 2 * 27 = 54 feet
Third side: x + 30 = 27 + 30 = 57 feet

Therefore, the dimensions of the triangle flower bed are:
Shortest side: 27 feet
Second side: 54 feet
Third side: 57 feet

138 = x + 2x + x + 30

108 = 4x
27 = x

The shortest side is 27. Take it from there.