Grid Paper Rectangles

Probability Level 3

How many rectangles are there in a 10 × \times 10 grid paper?

1000 3025 2025 550

Jh Yoon by JH Yoon , 20, South Korea

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Áron Bán-Szabó
Jun 30, 2017

Each rectangle has 4 sides. We will examine the sides' lines. From this 4 line, 2 are horizontal, and 2 vertical. There are 11 vertical and 11 horizontal grid line, so the answer is: ( 11 2 ) ∗ ( 11 2 ) = 5 5 2 = 3025 \binom{11}{2}*\binom{11}{2}=55^2=3025 .

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Hana Wehbi
Jun 30, 2017

The formula is ( n ( n + 1 ) 2 ) 2 = ( 10 × 11 2 ) 2 = 5 5 2 = 3025 (\frac{n(n+1)}{2})^2= (\frac{10\times11}{2})^2= 55^2 = 3025

1 Helpful 1 Interesting 0 Brilliant 0 Confused

For an m x n grid it is m n (m+1)*(n+1)/4

Vijay Simha - 2 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...