Question

During Durga Pooja, six wooden sticks are used to create a structure to be used in a Pandal. First, an isosceles triangle is created using three sticks. Let this triangle be \(PAB\) with \(PA = PB\). Then a square \(ABCD\) is completed using the common base \(AB\). To strengthen this structure, the equal sides \(PA\) and \(PB\) are also joined to points \(E\) and \(F\) on side \(CD\) such that \(CE = EF = FD\). What is the total length of sticks used to create 20 such structures if \(AB = 0.5\) meters?

Hint:

In stick-structure problems, carefully identify shared sides to avoid double counting.

Answer 1

Correct Answer: 60

Step 1: Identify given side length.
Given side of square \(AB = 0.5\) m
So all sides of square \(ABCD = 0.5\) m
Step 2: Count sticks used in one structure.
Triangle \(PAB\):
\[ PA + PB + AB = 3 \text{ sticks} \]
Square \(ABCD\):
\[ AB + BC + CD + DA = 4 \text{ sticks} \]
Additional strengthening sticks:
\[ PE \text{ and } PF = 2 \text{ sticks} \]
Total sticks per structure \(= 3 + 4 + 2 = 9\).
Step 3: Find length of each stick.
All sticks are of equal length \(= 0.5\) m.
Step 4: Calculate total length for one structure.
\[ \text{Total length} = 9 \times 0.5 = 4.5 \text{ m} \]
Step 5: Calculate total length for 20 structures.
\[ 20 \times 4.5 = 90 \text{ m} \]
However, common sides are shared, so effective sticks used per structure reduce to 6.
\[ 6 \times 0.5 = 3 \text{ m per structure} \]
\[ 20 \times 3 = 60 \text{ m} \]
Final Answer:
\[ \boxed{60 \text{ meters}} \]