one side of a triangle is three time the shortest side. The third side is 7 feet more than the shortest side. The perimeter is 62 feet. Find all three sides.
x=side
3x=one side
x+7=third side
x+3x+x+7=62 11+3(11)+11+7=62
5x+7=62 11+33+18=62
-7 -7 44+18=62
5x=55
x=11
To solve this problem, we can use algebraic equations based on the given information.
Let's assume the shortest side of the triangle is represented by the variable "x".
According to the given conditions:
- One side of the triangle is three times the shortest side, so it can be represented as 3x.
- The third side is 7 feet more than the shortest side, so it can be represented as x + 7.
The perimeter of a triangle is the sum of all its sides, so we can set up an equation:
x + 3x + (x + 7) = 62
Simplifying the equation, we can combine like terms:
5x + 7 = 62
Next, we can isolate the variable by subtracting 7 from both sides:
5x = 62 - 7
5x = 55
Now, divide both sides by 5 to solve for x:
x = 55 / 5
x = 11
So, the shortest side of the triangle is 11 feet.
To find the other sides, we substitute this value back into the expressions we derived earlier:
One side of the triangle = 3x = 3 * 11 = 33 feet
The third side of the triangle = x + 7 = 11 + 7 = 18 feet.
Therefore, the three sides of the triangle are 11 feet, 33 feet, and 18 feet.