Write the equation that represents the relationship between n the number of triangles and p the perimeter of the figures formed.
the triangle perimeters are 10 and the base is 7.
a.P=10n+14
b. P=10n+7
c.P=7n+10
d. P=7n+20.
the Perimeter of the triangles are 27. 34. 41.
Hey,, Please,, I really need help, I can't find my notes for this..
My answer as of right now is answer D, but I'm torn as well with B or C..
To find the equation that represents the relationship between the number of triangles (n) and the perimeter of the figures formed (p), we can use the given information.
Since the triangle perimeters are 10 and the base is 7, we can write the equation as:
P = 7n + 10
Now, let's substitute the given perimeters to find the corresponding number of triangles:
For P = 27, we have:
27 = 7n + 10
Subtract 10 from both sides:
17 = 7n
Divide both sides by 7:
n = 17/7
For P = 34, we have:
34 = 7n + 10
Subtract 10 from both sides:
24 = 7n
Divide both sides by 7:
n = 24/7
For P = 41, we have:
41 = 7n + 10
Subtract 10 from both sides:
31 = 7n
Divide both sides by 7:
n = 31/7
So, based on the given perimeters, the corresponding number of triangles are n = 17/7, n = 24/7, and n = 31/7.
However, we need to choose the correct equation that represents the relationship between n and p. Comparing the equation we derived P = 7n + 10 to the options provided:
a. P = 10n + 14
b. P = 10n + 7
c. P = 7n + 10
d. P = 7n + 20
The correct equation that represents the relationship is option c: P = 7n + 10.
To find the equation that represents the relationship between the number of triangles (n) and the perimeter of the figures formed (p), we need to analyze the given information.
From the statement "the triangle perimeters are 10, and the base is 7," we can conclude that each triangle has a base of length 7 and a perimeter of 10.
Now, let's consider the provided perimeters of the triangles, which are 27, 34, and 41. These perimeters can be obtained by adding the lengths of the three sides of each triangle.
From the information above, we can conclude that the equation representing the relationship between n and p is P = 10n + 21.
To verify this, substitute the given values of n (number of triangles) into the equation and check if the resulting perimeters match the provided values:
- For n = 3 (three triangles), P = 10(3) + 21 = 30 + 21 = 51 (not a match)
- For n = 4 (four triangles), P = 10(4) + 21 = 40 + 21 = 61 (not a match)
- For n = 5 (five triangles), P = 10(5) + 21 = 50 + 21 = 71 (not a match)
None of the given perimeters (27, 34, and 41) match the perimeters calculated using the equation P = 10n + 21. Therefore, none of the options (a, b, c, d) are correct.
It's important to note that the equation P = 10n + 21 is based on the given information and calculations. If any of the provided values were incorrect, the equation would change accordingly.