How many triangles and rectangles do three geometrical figures lying on the table have 10 vertices?

1) Determine how many triangles are on the table, if we know that it has 3 vertices, and there are 10 vertices of three geometric shapes on the table. We draw up an equation where:

X – triangles;

3 – X – rectangles;

10 – peaks.

3X + 4 (3 – X) = 10;

3X + 12 – 4X = 10;

-X = 10 – 12;

-X = -2;

X = 2 triangles.

2) Find out the number of rectangles lying on the table if we know that there are only 3 figures and 2 of them are triangles.

3 – 2 = 1 rectangle.

Answer: there are 2 triangles and 1 rectangle on the table.