The table shows the relationship between a, the area of a rectangle, and h, its height, when the base remains constant
H = 2, 5, 7, 12
A = 8 , 20, 28 48
Which equation represents the relationship between h and a
a = h + 6
a = 3h + 2
a = 4h
a = 2h + 4
Please explain answer choosen if different from (a = 4h)
Thanks you
As you can see from your table, a always equals 4h. There is nothing else to explain.
To determine which equation represents the relationship between h and a, we need to analyze the given data and find the pattern.
Looking at the table, we can see that the base remains constant (not given in the table), and we are given the values of h (height) and a (area). We can determine the relationship between h and a by observing the pattern of changes.
Let's evaluate the ratios of a to h for each corresponding pair of values:
- For the first pair: a/h = 8/2 = 4
- For the second pair: a/h = 20/5 = 4
- For the third pair: a/h = 28/7 = 4
- For the fourth pair: a/h = 48/12 = 4
From this analysis, we can conclude that for each pair, the ratio of a to h is consistently equal to 4. Therefore, the relationship between h and a can be represented by the equation a = 4h.
Now, let's compare this result to the other options given:
a = h + 6: This equation does not match the constant ratio observed in the table, so it is not correct.
a = 3h + 2: This equation also does not match the constant ratio observed in the table, so it is not correct.
a = 2h + 4: This equation also does not match the constant ratio observed in the table, so it is not correct.
Thus, based on the information provided, the equation that represents the relationship between h and a is a = 4h.