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  • 8 parallel lines intersecting 7 parallel lines can result in the formation of how many parallelograms?  Option: 1 732</d

8 parallel lines intersecting 7 parallel lines can result in the formation of how many parallelograms?

 

Option: 1

732


Option: 2

534


Option: 3

638


Option: 4

588


Answers (1)

best_answer

Given that,

There are 8 parallel lines intersecting 7 parallel lines.

We know that two parallel lines intersect other pairs of parallel lines to form a parallelogram, hence four lines are actually needed to create a parallelogram.

In order to implement how a parallelogram is built, we first select 2 parallel lines from the given 8 parallel lines, then multiply this result with the selection of 2 parallel lines from the 7 intersecting parallel lines. 

This will yield the potential number of parallelograms from 8 parallel lines intersecting 7 parallel lines.

The number of possible parallelograms from a set of 8 parallel lines is given by,

\mathrm{\begin{aligned} & { }^8 C_2=\frac{8 !}{2 ! 6 !} \\ & { }^8 C_2=\frac{8 \times 7}{2} \\ & { }^8 C_2=4 \times 7 \\ & { }^8 C_2=28 \end{aligned}}

The number of possible parallelograms from a set of 7 parallel lines is given by,

\mathrm{\begin{aligned} & { }^7 C_2=\frac{7 !}{2 ! 5 !} \\ & { }^7 C_2=\frac{7 \times 6}{2} \\ & { }^7 C_2=7 \times 3 \\ & { }^7 C_2=21 \end{aligned}}

Thus, the number of parallelograms formed from 8 parallel lines intersecting 7 parallel lines is,

\mathrm{\begin{aligned} & { }^8 C_2 \times{ }^7 C_2=28 \times 21 \\ & { }^8 C_2 \times{ }^7 C_2=588 \end{aligned}}

Therefore, the number of parallelograms formed is 588.

 

 

Posted by

Pankaj Sanodiya

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