The sides of a triangular lot are represented by x, 2x, and 3x + 2. Find each side if the perimeter is 362 feet.
What are the 3 lengths?
Solve the algebraic statement that the perimeter equals 362.
x + 2x + 3x + 2 = 6x +2 = 362
6x = 360
x = ___?
Once you have x, the three side lengths are easily compouted.
To find the lengths of the sides, we need to set up an equation based on the given information. Let's use the formula for the perimeter of a triangle, which states that the perimeter is the sum of all its sides.
Given that the sides of the triangular lot are represented by x, 2x, and 3x + 2, we can set up the equation:
x + 2x + (3x + 2) = 362
Simplifying the equation, we combine like terms:
6x + 2 = 362
Now, we isolate the variable x:
6x = 362 - 2
6x = 360
Dividing both sides by 6:
x = 360 / 6
x = 60
So, the first side length, represented by x, is 60 feet.
To find the lengths of the other two sides, we substitute the value of x back into the expressions given:
Side 1: x = 60 feet
Side 2: 2x = 2 * 60 = 120 feet
Side 3: 3x + 2 = 3 * 60 + 2 = 180 + 2 = 182 feet
Therefore, the lengths of the three sides of the triangular lot are 60 feet, 120 feet, and 182 feet.