Hi!
If the perimeter of the triangle is 41, then x is:
5x + 2 + 6x - 3 + 3x = 41
5x + 6x + 3x = 41 + 3 - 2
14x = 42
x = 42/14
x = 3
The x is 3.
I assume you are being asked to solve these equations. Since there wasn't an explanation as to how you are expected to solve them, I chose to demonstrate how to use a calculator matrix function. You can find matrix calculators online. My instructions are for a TI-84
Push the blue 2nd button then push x^-1 button (it says matrix above this button in blue)
Arrow over to edit to change the dimensions of the matrix and to put in your values. You have 3 equations (3 rows) and 4 terms (4 columns) so you put a 3x4 in for the dimension and the coefficients (see images).
You use the rref option in the math column in matrix to calculate the answer.
The numbers at the end are the solutions. x = -4, y = 2, z = -1
For number 1 the answer is 112
The area is the sum of 'n' rectangle areas.
The width of the rectangle is size of interval, (domain size)/n
The height of each rectangle is f(interval) as interval moves along domain.
For this example, domain size = 3-1 = 2
size of interval = 2/n
height varies from f(1) to f(3), increasing by 2/n each time.
f(1+(2/n)i)
Putting this together, the area is the sum of:

Since you are given the function f(x). Sub input into f(x) to get area in terms of n and i.

Finally, the summation is:
Answer:
60
Step-by-step explanation:
60 plus 60 plus 60 is 180
has to add up to 180