How do I write a polynomial expression to represent the third side of the triangle? I know one side is 2x-3y and the other is x+2y and P=5x+2y? I am lost.
I will assume that P represents the perimeter.
Let the third side be S
S + 2x-3y + x+2y = 5x + 2y
S = 5x+2y - 2x + 3y - x - 2y
= 2x + 3y
check:
What is the sum of (x+2y) + (2x-3y) + (2x+3y) ??
To find the polynomial expression for the third side of the triangle, we can use the fact that the perimeter of a triangle is the sum of the lengths of its three sides.
Given that one side of the triangle is 2x - 3y and the other side is x + 2y, we can write the equation for the perimeter (P) as:
P = (2x - 3y) + (x + 2y) + S,
where S is the third side of the triangle that we're trying to find.
We also know that P = 5x + 2y, according to the information given.
Now, let's rearrange the equation to solve for S:
5x + 2y = (2x - 3y) + (x + 2y) + S
Combining like terms on the right side:
5x + 2y = 3x - y + S
To isolate S, move 3x and -y to the left side of the equation:
5x + 2y - 3x + y = S
Simplifying the left side:
2x + 3y = S
Therefore, the polynomial expression for the third side of the triangle is 2x + 3y.
To find the third side of the triangle, you can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, you are given two sides:
1. First side: 2x - 3y
2. Second side: x + 2y
To represent the third side, let's call it "z". According to the triangle inequality theorem, we have the following relationship:
(2x - 3y) + (x + 2y) > z
Simplifying this inequality, we get:
3x - y > z
Since P = 5x + 2y, we can substitute P into the inequality:
3x - y > P
Now, to express "z" (or the third side) as a polynomial expression, we rearrange the inequality by isolating "z":
z < 3x - y
Therefore, the polynomial expression representing the third side of the triangle is:
z = 3x - y