Question

Based on the relationship between each polygon and the number inside it, the value of 'X' is ______. A triangle contains the number 6, a rectangle contains 24, a pentagon contains 120, and a hexagon contains X.

• A. 720
• B. 596
• C. 24
• D. 240

Hint:

Compare the number of sides of each polygon with the number written inside it.

Answer 1

The Correct Option is A

Step 1: List the number of sides of each polygon.
The triangle has \(3\) sides, the rectangle has \(4\) sides, the pentagon has \(5\) sides, and the hexagon has \(6\) sides.
Step 2: Compare each side count with its number.
Triangle: \(3\) sides, number shown is \(6\). Note that
\[ 3!=3\times2\times1=6 \]
Rectangle: \(4\) sides, number shown is \(24\). Note that
\[ 4!=4\times3\times2\times1=24 \]
Pentagon: \(5\) sides, number shown is \(120\). Note that
\[ 5!=5\times4\times3\times2\times1=120 \]
Step 3: Identify the pattern.
In every case, the number inside the polygon equals the factorial of the number of sides of that polygon.
Step 4: Apply the pattern to the hexagon.
The hexagon has \(6\) sides, so its value should be
\[ 6!=6\times5\times4\times3\times2\times1 \] \[ 6!=720 \]
Step 5: Final conclusion.
Therefore,
\[ \boxed{X=720} \]
Hence, the correct option is (A).