The longer side of a triangle is 3 times the shorter side. The third side is 4 inches longer than the shorter. How long is the short side if the perimeter is more than 39 inches?
If the shortest side is x, then we have
x + (x+4) + 3x > 39
5x > 35
x > 7
By the way, longer implies only two items. You want to use longest here, since a triangle has three sides.
Especially, since without knowing the value of x, maybe x+4 is bigger than 3x. The problem should simply have stated 2nd side and 3rd side.
To solve this problem, let's start by assigning variables to the shorter side and the longer side. Let's call the shorter side "x" inches.
According to the problem, the longer side is 3 times the shorter side, so the longer side can be represented as 3x inches.
The third side is 4 inches longer than the shorter side, so it can be expressed as x + 4 inches.
The perimeter of a triangle is the sum of all three sides. In this case, the perimeter is given to be more than 39 inches.
Therefore, we can write the equation for the perimeter as:
x + 3x + (x + 4) > 39
Simplifying the equation:
5x + 4 > 39
Subtracting 4 from both sides:
5x > 35
Dividing both sides by 5:
x > 7
So, the short side must be longer than 7 inches for the perimeter to be more than 39 inches.