Question

Alana draws four squares, five pentagons and six octagons. Marie draws n hexagons and notices that the combined number of diagonals in her hexagons is equal to the combined number of diagonals in Alana’s polygons. What is the value of n?

Answer 1

The value of n is 17.

Explanation:

We are given,

Alana draws 4 squares, 5 pentagons and 6 octagons.

Marie drew 'n' hexagons.

Also, the combined number of diagonals in Alana's polygons is equal to the combined number of diagonals in Marie's hexagons.

Since, the number of diagonals in a polygon is given by
`(n(n-3))/(2)`, where n is the number of sides.

So, using the formula, we have,

Number of diagonals in a square = 2

Number of diagonals in a pentagon = 5

Number of diagonals in a octagon = 20

Thus, total number of diagonals in Alana's polygons are 2×2 + 5×5 + 20×8 = 153.

Therefore, total number of diagonals in Marie's hexagons are 153.

As, number of diagonals in a hexagon = 9.

Total number of hexagons =
`(153)/(9)` = 17.

Hence, the value of n is 17.