A vacant city lot is being turned into a neighborhood garden. The neighbors want to fence in a triangular section of the lot and plant flowers there. The longest side of the triangular section is
44
feet shorter than twice the shortest side. The third side is
22
feet longer than the shortest side. The perimeter is
5858
feet. How long is each​ side?
(2s-44)+(s+22)+ s = 5858
4 s -22 = 5858
4 s = 5880
s = 1470 etc
Let's assume the shortest side of the triangular section is 'x' feet.
According to the given information, the longest side is 44 feet shorter than twice the shortest side, which can be expressed as:
Longest side = 2x - 44
The third side is 22 feet longer than the shortest side, which can be expressed as:
Third side = x + 22
The perimeter of a triangle is the sum of all three sides, which in this case is given as 5858 feet:
x + (2x - 44) + (x + 22) = 5858
Simplifying the equation, we have:
4x - 22 = 5858
Adding 22 to both sides:
4x = 5880
Dividing both sides by 4:
x = 1470
So, the shortest side is 1470 feet.
Now, we can find the longest and third sides:
Longest side = 2x - 44 = 2(1470) - 44 = 2916 - 44 = 2872 feet
Third side = x + 22 = 1470 + 22 = 1492 feet
Therefore, the lengths of the sides of the triangular section are:
Shortest side: 1470 feet
Longest side: 2872 feet
Third side: 1492 feet
To find the length of each side, we can set up equations based on the given information.
Let x be the length of the shortest side.
According to the problem, the longest side is 44 feet shorter than twice the shortest side. So, the length of the longest side is 2x - 44.
The third side is 22 feet longer than the shortest side, so the length of the third side is x + 22.
The perimeter of the triangle is the sum of the lengths of all three sides, which is 5858 feet. So, we can set up the equation:
x + (2x - 44) + (x + 22) = 5858
Simplifying the equation:
4x - 22 = 5858
Adding 22 to both sides:
4x = 5880
Dividing both sides by 4:
x = 1470
Now we can calculate the lengths of the other sides:
Longest side = 2x - 44 = 2(1470) - 44 = 2936 - 44 = 2892 feet
Third side = x + 22 = 1470 + 22 = 1492 feet
So, each side of the triangle has the following lengths:
Shortest side: 1470 feet
Longest side: 2892 feet
Third side: 1492 feet