Iwill give brainliest to whoever answers

90 cm^2

Step-by-step explanation:

The scale factor between triangle ABC and triangle PQR is 4:6 or  2:3

The scale factor is 2/3

When relating areas, we use the scale factor squared

Area of ABC = scale factor squared * Area of PQR

40 =  (2/3) ^2 Area of PQR

40  =4/9 Area of PQR

Multiply each side by 9/4

40 *9/4 = 9/4 *4/9 * Area of PQR

90 = Area of PQR

When we work with lengths of similar figures, we multiply by the scale factor.

When we work with areas of similar figures, we have a length and a width, so we are really multiplying by the scale factor two times, or the scale factor squared.

A = l*w

A = SF (l) * SF (w)

  = SF ^2 lw

So the area of the new  figure is the scale factor squared times the area of the old figure.

A new = SF^2 A old

To get from the old figure to the new figure we multiply by 6/4 or 3/2

A new =  (3/2)^2 (40)

A new = 9/4 * 40

           = 90

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.