Triangle PQR is congruent to P'Q'R. If PQ= x+y, P'Q'+10, Q'R'= 3x-y, and QR=14, then what is x and y?

Well, start setting stuff equal to each other

PQ = P'Q'
x+y = 10

QR = Q'R'
3x-y = 14

so, (x,y) = (6,4)

5 and 6

To find the values of x and y, we will use the fact that the corresponding sides of congruent triangles are equal in length.

Given that triangle PQR is congruent to triangle P'Q'R, we can set up the following proportional relationships between their corresponding sides:

PQ/P'Q' = QR/Q'R'
(x + y)/(x + 10) = 14/(3x - y)

We can solve for x and y by cross-multiplying and simplifying the equation:

14(x + 10) = (3x - y)(x + y)
14x + 140 = 3x^2 + 3xy - yx - y^2

Let's rearrange this equation to isolate the terms involving x and y on one side:

3x^2 + 3xy - yx - y^2 - 14x - 140 = 0

Now, we have a quadratic equation in terms of x and y. To solve for these variables, we need to provide additional information about the relationship between x and y. Without this information, we cannot solve for the specific values of x and y.