Question

In a shooting competition, all the shooters should hit the letter space in which letter 'A' is written as shown on the target board. The target board is a large equilateral triangle with each side 12 cm, and inside it the letter A is marked out as a smaller equilateral triangular space with each side 3 cm. What is the probability that the shooter will hit that space?

• A. 1/16
• B. 1/12
• C. 1/8
• D. 1/4

Hint:

Compare the letter-A triangle's side to the whole board's side; for similar triangles the area ratio is the square of the side ratio.

Answer 1

The Correct Option is A

Step 1: Model the board and the target space.
The whole target board is a large equilateral triangle of side 12 cm.
The letter-A space is a smaller equilateral triangle of side 3 cm.

Step 2: Connect probability to area.
For a shooter hitting a uniformly random point on the board, the probability of landing inside a region equals that region's area divided by the total area.

Step 3: Use the area ratio for similar triangles.
For two equilateral triangles, the ratio of their areas equals the square of the ratio of their sides.
\( \left(\dfrac{3}{12}\right)^{2} = \left(\dfrac{1}{4}\right)^{2} = \dfrac{1}{16} \).

Final Answer:
The probability of hitting the letter space is 1/16. \[ \boxed{\dfrac{1}{16}} \]