Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Find the number of rectangles an and Squares in chess 8 by 8 board respectively.​

Sagot :

genan

Answer:

squares: 204

rectangle: 1,296

Step-by-step explanation:

Board Size: 8 x 8

The total number of squares is thus:

[tex]1^{2} + 2^{2} + ... + n^{2}[/tex]

sum = [tex]\frac{n(n + 1)(2n + 1)}{6}[/tex]

For a chess board, with n = 8,

sum = [tex]\frac{(8)((8) + 1)(2(8) + 1)}{6}[/tex]

sum = 204

the number of rectangles on a chess board,

to make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. There are 36 distinct pairs and the same number of vertical pairs, so the answer is 36 × 36 = 1,296.

View image genan
View image genan
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.