Question

There are a total of 38 triangles and squares. If you count all sides of those triangles and squares, there are 134 sides. How many triangles? How many squares?

Answer 1

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.