0

Guest

Courses New

The 9 horizontal and 9 vertical lines on an 8X8 chessboard form 'r' rectangles& 's' squares. The ratio of s/r in the lowest terms is?

The 9 horizontal and 9 vertical lines on an 8X8 chessboard form 'r' rectangles& 's' squares. The ratio of s/r in the lowest terms is?

Grade:12

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear jee king

number of rectangles = r = 9C2 *9C2  =1296

number of square=s = (12 + 22 + 32 + ................+ 82 ) =204

 

so s/r =204/1296

Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin

 

Spandan Mallick
12 Points
5 years ago
First for squares,
We see in a 8×8 chessboard, there are 64, 1×1 squares. Similarly 32, 2×2 squares and 16, 3×3 squares. Hence it forms a pattern. Also if you divide the area... total area is 64 sq. units. 
For 1×1 squares, hence 64 are possible. For 2×2squares you can get it. Hence,
No of squares = (12+22+32+...+82) = 204.
For rectangles, consider the number of lines rather than squares. There are 9 lines. A rectangle can be formed by combination of any of these two four lines taking two from each pair of 9. Hence,
9C2 × 9C2 = 1296.
 
Spandan Mallick, IIT-JEE Aspirant

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More