A chessboard has diagnols of length 40 cm. What is the length of each side of the board?

Question

use the phythogrean theorem and solve to the nearest tenth.

 

Answer 1

Keep in mind that a Chessboard is square, which means sides A & B for your Pythagorean Theorem will be the same.

 

Since the theorem is a²+b²=c², you can change it in this case because a=b. So your new formula would be 2a²=c².

 

Your c value is 40cm beacause c=length of the hypotenuse, or in this case the diagonal of the chess board.

 

You now have 2a²=40².

 

Start solving it:

 

2a²=40²

2a²=1600

(2a²)/2=1600/2

a²=800

√(a²)=√800

a=√800 cm

 

You can plug this back in to check your answer, and also be sure that a=b is true.

 

a²+b²=c²

(√800)²+(√800)²=c²

800+800=c²

1600=c²

√1600=√c²

40=c