Answer: 13 triangles were used.
Step-by-step explanation:
Each triangle has 3 sides where each square has 4 sides.
Total triangles and squares = 17
Total sides they have = 64
Let x= Number of triangles , y= Number of squares
3x = sides of all triangles , 4x = Sides of all squares.
Now, [tex]x+y=17\ \ \ \ (i)[/tex]
[tex]3x+4x=64\ \ \ \ \ (ii)[/tex]
Multiply 3 on both sides of (i) , we get
[tex]3x+3y = 51\ \ \ \ (iii)[/tex]
Eliminate (ii) from (ii)
x= 13
Put this in (i), we get
[tex]13+y=17\\\\\Rightarrow\ y= 17-13=4[/tex]
Hence, 13 triangles were used.
There were 4 triangles used to frame a geometric pattern
Two are more equations that shares common variables are the system of equations. System of equations can be solved by using elimination method or substitution method .
Use the given information to frame system of equations.
Assume variables for the unknown
Let x be the number of triangles used and 'y' be the number of squares used
A geometric pattern is made using 17 triangles and squares.
Sum of triangles and squares is equal to 17
[tex]x+y=17[/tex]
the triangles and squares have a total of 64 sides,
Each triangle has 3 sides and each square has 4 sides
[tex]3x+4y=64[/tex]
Solve both the equations using substitution method
[tex]x+y=17\\y=17-x[/tex]
Substitute y in second equation
[tex]3x+4y=64\\3x+4(17-x)=64\\3x+68-4x=64\\-1x+68=64\\-1x=64-68\\-1x=-4\\x=4[/tex]
Now find out y
[tex]y=17-x\\y=17-4\\y=13[/tex]
'x' is the number of triangles used
x=4, so 4 triangles were used
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