The perimeter of a triangle is 44 cm. one of its sides is 4 cm smaller than the other and twice as long as the third side. find the sides of the triangle.

Perimeter of a triangle=sum of all sides.
We have three sides in a triangle;
The third side is : x
The second side is:2x
The first side is : 2x+4
Then we have the following equation.
x+2x+(2x+4)=44
5x=40
x=40/5
x=7

The third side is x=8
The second side is 2x=2*8=16
The first side is: 2x+4=2*8+4=20

The sides of the triangle would be: 8 cm, 16 cm and 20 cm

{13, 17, 12, 21, 18, 20} has the greatest spread for the middle 50% of its data.

Step-by-step explanation:

Given:

Set 1={18, 13, 22, 17, 21, 24}

Set 2={17, 19, 22, 26, 17, 14}  

Set 3= {13, 17, 12, 21, 18, 20}

Set 4=  {18, 21, 16, 22, 24, 15}

To find :

Data set has the greatest spread for the middle 50% of its data=?

Solution:

Step 1:  Re arranging the data sets in ascending order

Re-arranging data-set 1 we get,

{13, 17, 18, 21, 22, 24}

Re-arranging data-set 2 we get,

{14, 17, 17, 19, 22 , 26}

Re-arranging data-set 3 we get,

{12, 13, 17, 18, 20, 21}

Re-arranging data-set 4 we get,

{15, 16,18, 21, 22, 24}

Step 2 : Finding the interquantile region:

Interquantile Range(IQR) = lower median-upper median

For data-set 1

IQR=22-17=5

For data-set 2

IQR=22-17=5

For data-set 3  

IQR=20-13=7

For data-set 4

IQR=22-16=6

Hence the data set 3 = {13, 17, 12, 21, 18, 20} has greatest spread for the middle 50% of its data .