Candace S. answered • 02/28/16
Tutor
4.9
(28)
A day without Math is like a day without sunshine!
Hi Angela,
The three sides of the isosceles triangle are x, x, and (x+x-4)=(2x-4).
The perimeter will be the sum of all three sides: x+x+(2x-4)
=4x-4
Since the perimeter is less than 80cm, the inequality is: 4x-4<80
Solving the inequality: 4x-4<80
Add 4 to each side: 4x<84
Divide by 4: x<24
What are the possible lengths of the equal sides?
Since x in an integer less than 24, then x is an element of the set {1,2,3,...,23}
Since x is the length of a side of a triangle, x cannot be zero or negative integers.
But we need to make sure that the x value takes into mind the length of the third side of length 2x-4.
solve 2x-4=0
x=2
As stated before you cannot have zero length of a triangle, so x>2.
These leaves you with the set of x values: {3,4,5,...,22,23}
The lengths of the smallest triangle are 3, 3, 2 with a perimeter of 8.
Now we need to check the upper value of x.
The lengths of the largest triangle are 23, 23, 42 with a perimeter of 88 >80 cannot be in the set.
22, 22, 40 with a perimeter of 84 >80
21, 21, 38 with a perimeter of 80; this won't work because the question ask for the perimeter to be less than 80. So it must be 20.
20, 20, 36 with a perimeter of 76
Final Answer: the set of possible x values are {3, 4, 5,..., 19, 20}. Using inequalities x is an integer 3 <= x <=20
