the first side of a triangle measures 3 cm longer then the second side the third side is 4cm shorter then twice the second side the perimeter is 31cm. how long is each side?
second side = s
s+3
s
2s-4
s+3+s + 2s - 4 = 31
4 s = 32
s = 8
so
11
8
12
858648648
To find the lengths of the sides of the triangle, let's assign variables to the sides:
Let the second side of the triangle be x cm.
The first side will then be x + 3 cm.
The third side will be 2x - 4 cm, as it is 4 cm shorter than twice the second side.
According to the question, the perimeter of the triangle is 31 cm. We can use this information to set up an equation:
Perimeter = Sum of all three sides
31 cm = x + (x + 3) + (2x - 4)
Now, let's solve the equation to find the value of x:
31 cm = 4x - 1
Adding 1 to both sides of the equation:
32 cm = 4x
Dividing both sides by 4:
8 cm = x
Now that we know the value of x, we can substitute it back into our earlier equations to find the lengths of all three sides:
First side = x + 3 = 8 + 3 = 11 cm
Second side = x = 8 cm
Third side = 2x - 4 = 2(8) - 4 = 12 cm
So, the lengths of the sides of the triangle are:
First side: 11 cm
Second side: 8 cm
Third side: 12 cm