Answer:
The first step is to make the system of equations.
First, the triangle:
x + 3x + 7y = 41, so 4x + 7y = 41
Then the rectangle:
2(7y + 3x) = 66, so 7y + 3x = 33
We have a 7y in each equation.. so let's isolate it.
Triangle equation we have: 7y = 41 - 4x
Rectangle equation we have: 7y = 33 - 3x
We have A = B and A = C ... so we can say C = B, and join those two equations:
33 - 3x = 41 - 4x, we add 4x and substract 33 on each side to get
4x - 3x = 41 - 33... so x = 8
Now that we know the value of x, we replace it in either of the two equations:
7y = 41 - 4 (8) = 41 - 32 = 9
y = 9/7
We can then determine easily the sides of each figure:
Triangle:
x, 3x, 7y become (8), (3 * 8), (7 * 9/7) so... 8, 24, 9, which sums up to 41.
Rectangle:
7y, 3x become (7 * 9/7) and (3*8) = 9 and 24, which sums up to 33... so perimeter of 66 is confirmed.
