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 11 feet mre then the length of the shortest side. find the dimmenstions if the perimter is 163feet
163 = x + 2x + x + 11
152 = 4x
x = 38
38 + 76 + 49 = 163
Let's assume the length of the shortest side of the triangle is "x" feet.
According to the given information, the second side of the triangle is twice the length of the shortest side, so its length would be "2x" feet.
The third side of the triangle is 11 feet more than the length of the shortest side, so its length would be "x + 11" feet.
To find the perimeter of the triangle, we need to sum up the lengths of all three sides:
Perimeter = x + 2x + (x + 11)
According to the question, the perimeter is equal to 163 feet:
163 = x + 2x + (x + 11)
Simplifying the equation:
163 = 4x + 11
Subtracting 11 from both sides:
152 = 4x
Dividing both sides by 4:
x = 38 feet
So, the length of the shortest side is 38 feet.
Using this information, we can find the lengths of the other sides:
Second side: 2x = 2 * 38 = 76 feet
Third side: x + 11 = 38 + 11 = 49 feet
Therefore, the dimensions of the flower bed are:
Shortest side: 38 feet
Second side: 76 feet
Third side: 49 feet
To find the dimensions of the flower bed, we'll need to set up and solve an equation based on the given information.
Let's start by assigning variables to the sides of the triangle. Let's call the shortest side "x".
According to the given information:
- One side of the triangle is twice the length of the shortest side, so this side would be 2x.
- The third side is 11 feet more than the length of the shortest side, so this side would be x + 11.
The perimeter of a triangle is the sum of all its sides. So, we can write the equation:
x + 2x + (x + 11) = 163
Simplifying the equation, we combine like terms:
4x + 11 = 163
Next, we isolate the variable:
4x = 163 - 11
4x = 152
Finally, we solve for x by dividing both sides of the equation by 4:
x = 152 / 4
x = 38
So, the shortest side of the flower bed is 38 feet.
Now, we can find the dimensions of the flower bed:
- The shortest side is 38 feet.
- One side is twice the length of the shortest side: 2x = 2 × 38 = 76 feet.
- The third side is 11 feet more than the shortest side: x + 11 = 38 + 11 = 49 feet.
Therefore, the dimensions of the flower bed are 38 feet, 76 feet, and 49 feet.