answer : 18 triangles and 20 squares.
We have two pieces of information:
The total number of shapes is 38:
T + S = 38
The total number of sides is 134, with triangles having 3 sides and squares having 4 sides:
3T + 4S = 134
Now, we can use these equations to solve for T and S. First, let's simplify the second equation by dividing both sides by 1:
3T + 4S = 134
Now we have a system of two equations:
T + S = 38
3T + 4S = 134
We can solve this system of equations using various methods, such as substitution or elimination. Let's use the elimination method by multiplying the first equation by 3 to make the coefficients of T in both equations equal:
(3T + 3S = 114) [Multiply the first equation by 3]
Now, we have:
3T + 4S = 134
3T + 3S = 114
Subtract the second equation from the first equation to eliminate T:
(3T + 4S) - (3T + 3S) = 134 - 114
This simplifies to:
S = 20
Now that we know the number of squares (S), we can substitute it back into the first equation to find the number of triangles (T):
T + 20 = 38
Subtract 20 from both sides:
T = 38 - 20
T = 18
So, there are 18 triangles and 20 squares.