Question

Emily counts the triangles and parallelograms in an art piece and determines that in

parallelograms. If there are 150 total sides, how many triangles and para
ograms in an art piece and determines that there are altogether 42 triangles and

Answer 1

There are 18 triangles and 24 parallelograms.

Explanation:

Let the number of Triangles be x

and number of Parallelograms be y

By given data;

There are together 42 triangles and parallelogram

`x+y=42\\x=42-y`

Also there are 150 total sides,

Now we know that triangle have 3 side and parallelogram consist of 4 sides.

Hence the equation will become:
`3x+4y =150`

Now substituting value of x in above equation we get;

`3(42-y)+4y=150\\126-3y+4y=150\\y=150-126=24`

Hence
`x=42-y=42-24=18`

Hence, there are 18 triangles and 24 parallelograms.