one side of a triangle is 2cm shorter than the base The ofther side is 3cm longer than the base what lengths of the base will allow the perimeter to be greater than 19 cm?
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
Let's assume the length of the base of the triangle is "x" cm.
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.
To find the lengths of the base that will allow the perimeter to be greater than 19 cm, we need to set up and solve an inequality.
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.