One side of a triangle is three times the shortest side. The third side is 7 feet more than the shortest side. The perimeter is 62 feet. Find all three sides.
side 1= 3x
side 2= x
side 3= x+7
3x + x + x+7 = 62
5x = 55
x=11
side 1= 3(11) = 33
side 2= (11) = 11
side 3= (11)+7 = 18
To solve this problem, we will use the given information to set up a system of equations and solve it to find the lengths of all three sides of the triangle.
Let's denote the shortest side as x.
Given that one side of the triangle is three times the shortest side, we can say that the second side is 3x.
Also, the third side is 7 feet more than the shortest side, so it would be x + 7.
The perimeter of a triangle is the sum of the lengths of all three sides, so we can set up the equation:
x + 3x + (x + 7) = 62
Now, let's solve this equation to find the value of x:
x + 3x + x + 7 = 62
5x + 7 = 62
5x = 62 - 7
5x = 55
x = 55 / 5
x = 11
So, the shortest side of the triangle is 11 feet.
The second side is 3 times the shortest side, which is 3 * 11 = 33 feet.
The third side is 7 feet more than the shortest side, which is 11 + 7 = 18 feet.
Therefore, the lengths of the three sides are 11 feet, 33 feet, and 18 feet.