Suppose you want to build a rectangular sandbox where the width is 7 less than the length and the diagonal is 2 feet longer than the length. what are the dimensions of the sandbox?

The dimensions of the sandbox will be 15 feet by 8 feet.

Step-by-step explanation:

Suppose we want to build a rectangular sandbox where the width is 7 less than the length and the diagonal is 2 feet longer than the length.

If x is the length and y is the width in feet, then we have the equations  

x - y = 7 ......... (1) and  

........ (2)

Now, solving equations (1) and (2) we get

⇒

Now, squaring both sides we get,

x² + x² - 14x + 49 = x² + 4x + 4

⇒ x² - 18x + 45 = 0

⇒ (x - 15)(x - 3) = 0

⇒ x = 15 or 3

But from equation (1) x ≠ 3, then x = 15 and y = x - 7 = 8

Therefore, the dimensions of the sandbox will be 15 feet by 8 feet. (Answer)

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.

there are infinitely many solutions.