let base be x
one other side = x-2
third side = x+3
x + x-2 + x+3 > 19
3x > 18
x > 6
test: let base be 7
one other side = 5
third side = 10
perm = 22
one other side = x-2
third side = x+3
x + x-2 + x+3 > 19
3x > 18
x > 6
test: let base be 7
one other side = 5
third side = 10
perm = 22
According to the given information, one side of the triangle is 2 cm shorter than the base, so its length would be (x - 2) cm.
The other side of the triangle is 3 cm longer than the base, so its length would be (x + 3) cm.
To calculate the perimeter of the triangle, we add the lengths of all the sides:
Perimeter = Base + Side1 + Side2
Perimeter = x + (x - 2) + (x + 3)
Perimeter = 3x + 1
Given that the perimeter needs to be greater than 19 cm, we can set up the inequality:
3x + 1 > 19
Now, let's solve this inequality for x:
3x > 19 - 1
3x > 18
x > 18/3
x > 6
So, the length of the base needs to be greater than 6 cm for the perimeter to be greater than 19 cm.
Let's assume the length of the base is "x" cm.
According to the given information:
- One side of the triangle is 2 cm shorter than the base, so it will have a length of (x - 2) cm.
- The other side of the triangle is 3 cm longer than the base, so it will have a length of (x + 3) cm.
The perimeter of the triangle is the sum of all three sides, so we can calculate it by adding the lengths of the sides:
Perimeter = x + (x - 2) + (x + 3)
Perimeter = 3x + 1
To ensure the perimeter is greater than 19 cm, we can set up the following inequality:
3x + 1 > 19
Now, we can solve this inequality to find the valid lengths of the base:
3x > 18 (subtracted 1 from both sides)
x > 6 (divided both sides by 3)
Therefore, the base should have a length greater than 6 cm for the perimeter to be greater than 19 cm.