a flower bed is the shape of a triangle with one side twice the length of the shortest side and the third side is 30 ft more than the shortest side. find the dimentions if the perimeter is 102 ft.
x = shortest side
2x = 2nd side
x + 30 = 3rd side
x + 2x + x + 30 = 102
Solve for x, and use to determine the dimensions as defined above
Let's denote the shortest side of the triangle as "x" ft.
According to the given information, the second side of the triangle is twice the length of the shortest side, so it would be 2x ft.
The third side of the triangle is 30 ft longer than the shortest side, so it would be x + 30 ft.
To find the perimeter of the triangle, we add up all three sides:
Perimeter = x + 2x + x + 30
We are given that the perimeter is 102 ft, so we can write the equation:
102 = x + 2x + x + 30
Simplifying the equation:
102 = 4x + 30
Subtracting 30 from both sides:
72 = 4x
Dividing both sides by 4:
x = 18
So, the shortest side of the triangle is 18 ft, the second side is twice the shortest side which is 2 * 18 = 36 ft, and the third side is 30 ft longer than the shortest side which is 18 + 30 = 48 ft.
To solve this problem, let's assume the length of the shortest side of the triangle is x ft.
According to the given information, one side of the triangle is twice the length of the shortest side. Therefore, the length of this side would be 2x ft.
The third side is 30 ft more than the shortest side, so its length would be x + 30 ft.
The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is 102 ft.
Using the information we have, we can write the equation for the perimeter as:
x + 2x + (x + 30) = 102
Simplifying the equation:
4x + 30 = 102
Next, let's isolate x by moving 30 to the other side of the equation:
4x = 102 - 30
4x = 72
Now, divide both sides of the equation by 4 to solve for x:
x = 72 / 4
x = 18
We have found that the shortest side (x) is 18 ft.
Now we can find the lengths of the other two sides:
One side is twice the length of the shortest side: 2x = 2 * 18 = 36 ft.
The other side is 30 ft more than the shortest side: x + 30 = 18 + 30 = 48 ft.
Therefore, the dimensions of the flower bed are:
Shortest side: 18 ft
Second side: 36 ft
Third side: 48 ft