Question

Can anyone answer this for me?

Answer 1

For 19 to 21:

All you need to do is count the spaces between each line of the numerator and then the same with the denominator.

19. You can see that there are 4 spaces between Point A and Point B. There are 6 spaces between point A and Point C. So if you will get ratio you will get:

$\frac{4}{6}$ Then you simplify the expression.
$\frac{2}{3}$

20. There are 2 spaces from points B to C. There are 3 spaces from points C to D. So the ration then will be:
$\frac{2}{3}$ 

This is already in its simplest form. You may be wondering why we did not count from 0. This is because the reference point for the two lines are given. For the first it is B and for the second is C.

21. Moving on to number 21. The distance from point B to D is 5 spaces, and the distance from point A to E is 12 spaces. So you can say that the ratio would be:

$\frac{5}{12}$ Again, this is already in its simplest form. 

22. To get the geometric mean between two numbers you first need to multiply them and then get the square root:

STEP 1: Multiply 7 and 28
                            7 x 28 = 196
STEP 2: Get the square root of the product
              √196 = 14

14 is the geometric mean.

23. Simplifying ratios is relatively easy. When you simplify the ratio between two values that are of different units, you first need to make both units the same. 
In your case, we need to either convert 10ft to inches or convert 30 inches to feet. So we will not come up with a decimal, let us just convert 10 ft into inches. 

$10 ft$ x $\frac{12in}{1ft}$ = 120 inches

So our new ratio is:
$\frac{120in}{30in}$
Now we simplify it to its simplest form:
$\frac{4in}{1in}$

24. The two figures are what we call similar figures. This means that the lengths of each side are proportional to their corresponding sides. 

AB is proportional to line FG. 
AB = 4 and FG =8
This means that the sides of ABCDE is half the lengths of the sides of FGHJK. Thus we can say that the perimeter of ABCDE is half the perimeter of FGHJK
To get the perimeter of a polygon, all you have to do is add all the sides. 
Let's get the perimeter of FGHJK
8 + 8 + 10 + 12 + 10 = 48
Half of 48 =24 
So the perimeter of ABCDE is 24

If you want to double check your answer you can get the sides of polygon of ABCDE by getting half of each corresponding side. 
AB = 4
BC = 4
CD = 5
DE = 6
EA = 5

If you get the sum of all sides, you can get the perimeter:
4 +4 +5 + 6 + 5 = 24

Answer 2

For 24, the answer is 24.