https://file.aiquickdraw.com/mathbot/file/1726901016151lbe78pzb.jpg

The problem you've provided involves identifying a matchstick pattern. Based on the shapes and choices given, we can break it down:

1. Each shape appears to represent a house, consisting of two parts: a square (with 4 matchsticks) and a triangular roof (with 3 matchsticks).
2. For each additional house, a few matchsticks are shared between adjacent shapes, reducing the total number of matchsticks required.

Let’s analyze the problem:
- One house (square + triangle) requires 7 matchsticks.
- Two houses share one side of the square, so the number of matchsticks will be fewer than double the original amount.
- As we increase the number of houses, the total number of matchsticks follows a pattern.

The answer choices represent the total number of matchsticks as a function of the number of houses, \( n \):
- (a) \( m + 5 \)
- (b) \( m + 6 \)
- (c) \( m + 5 \)
- (d) \( m + 8 \)

Since there is a mark next to option (b), which is \( m + 6 \), this suggests that the correct pattern likely involves adding 6 matchsticks for every additional house beyond the first.

### Correct Answer: \( m + 6 \)

Would you like further explanation or details about this approach?

Here are 5 related questions to expand your understanding:
1. How many matchsticks are required for 4 houses in the same pattern?
2. What is the general formula for the number of matchsticks needed for \( n \) houses in this setup?
3. How does the number of shared matchsticks between adjacent houses affect the total count?
4. Can we apply the same concept to different shapes, such as pentagons or hexagons?
5. What would the matchstick count be if each house had a different number of matchsticks for the roof and base?

**Tip**: Identifying patterns is key to solving problems with repeated elements like matchsticks, tiles, or other sequential structures.

Determine the total number of matchsticks used to form a pattern of houses. The pattern shows multiple houses, with the number of matchsticks represented by options (a) m + 5, (b) m + 6, (c) m + 5, (d) m + 8.

Learn how to calculate the total number of matchsticks used in a house pattern. This problem focuses on pattern recognition and arithmetic sequences, suitable for students in Grades 4-6.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation