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 18 feet more than the length of the shortest side. Find the dimensions if the perimeter is 142 feet.
P = a + b + c
Let a = shortest side
b = 2a
c = a + 18
142 = a + 2a + a + 18
142 = 4a + 18
124 = 4a
31 = a
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 18 feet more than the length of the shortest side. Find the dimensions if the perimeter is. 134 feet.
Let's assume that the shortest side of the triangle is x feet.
According to the problem, one side of the triangle is twice the length of the shortest side. So, the second side would be 2x feet.
The third side is 18 feet more than the length of the shortest side. Therefore, the third side would be x + 18 feet.
To find the perimeter of the triangle, we add up all three sides:
Perimeter = shortest side + second side + third side
Substituting the values we have:
142 = x + 2x + (x + 18)
Simplifying the equation:
142 = 4x + 18
Subtracting 18 from both sides:
124 = 4x
Dividing both sides by 4:
x = 31
Now, we have the value of x, which represents the shortest side of the triangle.
The second side is twice the length of the shortest side:
2x = 2 * 31 = 62 feet
The third side is 18 feet more than the shortest side:
x + 18 = 31 + 18 = 49 feet
Therefore, the dimensions of the flower bed are:
Shortest side: 31 feet
Second side: 62 feet
Third side: 49 feet
To solve this problem, let's break it down step by step:
Step 1: Define the variables
Let's denote the length of the shortest side as "x" feet.
Step 2: Express the other sides in terms of x
According to the problem statement,
- One side is twice the length of the shortest side, so it can be expressed as 2x.
- The third side is 18 feet more than the length of the shortest side, so it can be expressed as x + 18.
Step 3: Write the equation for the perimeter
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is given as 142 feet, so we can write the equation:
x + 2x + (x + 18) = 142
Step 4: Solve the equation
Combine like terms:
4x + 18 = 142
Subtract 18 from both sides:
4x = 142 - 18
4x = 124
Divide both sides by 4:
x = 124 / 4
x = 31
Step 5: Find the dimensions
Now that we have the value of x, we can find the dimensions of the triangle:
- The shortest side is x = 31 feet
- The second side is 2x = 2 * 31 = 62 feet
- The third side is x + 18 = 31 + 18 = 49 feet
So, the dimensions of the triangle are:
Shortest side: 31 feet
Second side: 62 feet
Third side: 49 feet