Answer:
We know that in a scalene triangle all sides (and angles) are different.
Let
z = length of longest side
y = length of second side
x = length of shortest side
The perimeter of the scalene triangle is 60 cm
x + y + z = 60 cm
The length of the longest side is 4 times that of the shortest side.
z = 4*x
We are left with the following equations
x + y + z = 60
z = 4*x
We will test every affirmation
Number one
The value of x can equal 40.
FALSE. The longest side cannot be greater than the perimeter.
Number two
The longest side can equal 30 cm
z = 30 cm
x = 30/4 cm = 7.5 cm
y = [60 -30 - 7.5] cm = 22.5 cm
This statement is TRUE
Number three
The shortest side can equal 7 cm
x = 7 cm
z = 4*7 cm = 28 cm
y = [60 -28 - 7] cm = 25 cm
This statement is TRUE
Number four
The value of x can equal 25
x = 25 cm
z = 4*25 cm = 100 cm
The longest side cannot be greater than the perimeter.
This statement is FALSE
Number five
The shortest side can equal 5
x = 5 cm
z = 4*5 cm = 20 cm
y = [60 -20 - 5] cm = 35 cm
This statement is FALSE. The second side (y) cannot be greater than the longest side (z).
