Question

The area of this triangle, A, is equal to the perimeter of this triangle.

Create a system of equations to model this situation. Determine if there are any solutions, and, if possible, whether or not they are viable.


How many total possible solutions are there to this system?

a.) No possible solutions
b.) One possible solution
c.) more than two possible solutions
d.) two possible solutions


Of any possible solutions, how many are viable solutions for this situation?

Answer 1

The perimeter is the sum of the sides:
P = (x-7) + (x + 1) + (x)
Rewriting:
P = 3x - 6
The area is given by:
A = (1/2) * (x-7) * (x)
The area and the perimeter are the same:
(1/2) * (x-7) * (x) = 3x - 6
Rewriting:
(x-7) * (x) = 6x - 12
x ^ 2-7x = 6x - 12
x ^ 2 - 7x - 6x + 12 = 0
x ^ 2 - 13x + 12 = 0
Polynomial of degree 2, therefore there are 2 possible solutions.
Viable solutions:
x = 12
Sides of the triangle:
5
12
13
Answer:
d.) two possible solutions
One viable solution