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 14 feet more than the length of the shortest side. Find the dimensions if the perimeter is 158 feet
s + 2s + s + 14 = 158
4s = 144
s = 36
shortest side = 36
side 2 = 72
side 3 = 50
Why did the flower bed cross the road? To get to the other side of the garden! Okay, let's solve this.
Let's say the length of the shortest side is x.
According to the problem, the second side is twice the length of the shortest side which means it is 2x.
The third side is 14 feet more than the length of the shortest side, so it will be x + 14.
To find the perimeter, we add up the lengths of all three sides:
x + 2x + (x + 14) = 158
Combining like terms, we get:
4x + 14 = 158
Now, let's subtract 14 from both sides:
4x = 144
Divide both sides by 4:
x = 36
So, the shortest side is 36 feet, the second side is 72 feet (double the shortest side), and the third side is 50 feet (36 + 14).
Let's let the shortest side of the triangle be represented by "x" feet.
The second side is twice the length of the shortest side, so it would be 2x feet.
The third side is 14 feet more than the shortest side, so it would be x + 14 feet.
To find the perimeter, we add up the lengths of all three sides:
Perimeter = x + 2x + (x + 14) = 4x + 14
Given that the perimeter is 158 feet, we can set up the following equation:
4x + 14 = 158
Subtracting 14 from both sides:
4x = 144
Dividing both sides by 4:
x = 36
Now we can find the lengths of all three sides:
Shortest side: x = 36 feet
Second side: 2x = 2 * 36 = 72 feet
Third side: x + 14 = 36 + 14 = 50 feet
Therefore, the dimensions of the triangle flower bed are:
Shortest side: 36 feet
Second side: 72 feet
Third side: 50 feet
To find the dimensions of the triangle flower bed, let's denote the length of the shortest side as x.
According to the given information, one side of the triangle is twice the length of the shortest side, which means one side has a length of 2x.
The third side is 14 feet more than the length of the shortest side, so it has a length of x + 14.
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is given as 158 feet, so we can write the equation:
x + 2x + (x + 14) = 158
Now, let's solve the equation:
4x + 14 = 158
Subtracting 14 from both sides:
4x = 144
Now divide both sides by 4:
x = 36
So, the shortest side has a length of 36 feet.
Substituting this value into the expressions for the other sides:
2x = 2 * 36 = 72 (length of the second side)
x + 14 = 36 + 14 = 50 (length of the third side)
Therefore, the dimensions of the triangle flower bed are:
Shortest side: 36 feet
Second side: 72 feet
Third side: 50 feet