(30 points!) The lengths of the sides of a triangle are in the extended ratio 4:7:9. The perimeter is 60cm. What are the lengths of the sides?

The lengths of the sides are 12cm, 28cm and 36cm.

Step-by-step explanation:

Let the smallest side be 4x, the middle side be 7x and the largest side be 9x.

Smallest side + middle side + largest side = 60cm

4x + 7x + 9x = 60

20x = 60

x = 60 ÷ 20

x = 3

Smallest side (4x) = 3 × 4

                             = 12

Middle side (7x)  = 7 × 4

                           = 28

Largest side (9x) = 9 × 4

                            = 36

Table of ordered data

number of       value
data

1                      62
2                      88
3                      89
4                      90
5                      92
6                      95
7                      96
8                      98
9                    100
10                  100

Range of scores: 100 - 62 = 38

Oulier: 62 => Range without the outlier = 100 - 88 = 12

Interquartile range, IQR, = difference between third quartile and first quartile: IQR = Q3 - Q1

Quartlies of all the data:

1                      62
2                      88
3                      89   first quartile, Q1 = 89
4                      90
5                      92
median, Q2 = (95 + 92) / 2 = 93.5
6                      95
7                      96
8                      98 third quartile, Q3 = 98
9                    100
10                  100

=> IQR = 98 - 89 = 9 : the interquartle range is 9

Quartlies without the outlier:

2                      88
3                      89
first quartile, Q1 = (89 + 90) / 2 = 89.5
4                      90
5                      92
6                      95 median, Q2 = 95
7                      96
8                      98
third quartile, Q3 = (98 + 100) / 2 = 99
9                    100
10                  100

=> IQR = Q3 - Q1 = 99 - 89.5 =  : the interquartle range without the outlier is 9.5

Therefore, the outlier impacts more the range than it impacts the IQR.

THE ONLY STATEMENT THAT IS FALSE IS THE NUMBER 5.