Question

The perimeter of the scalene triangle is 60 cm. The length of the longest side is 4 times that of the shortest side. Which statements about the possible measures of the sides are reasonable? Check all that apply. The value of x can equal 40. The longest side can equal 30 cm. The shortest side can equal 7 cm. The value of x can equal 25. The shortest side can equal 5.

Answer 1

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).