The diagonal of the square is √(34^2 + 34^2)
= √2312 inches
so what is your verdict?
repeat for the other one. Suggestion, do not use decimals
Which table has a diagonal whose length (measured in inches) is an irrational number? What is the length of this diagonal?
= √2312 inches
so what is your verdict?
repeat for the other one. Suggestion, do not use decimals
For the square table:
Side length = 34 inches
The formula for the diagonal of a square is given by:
Diagonal = √(Side length^2 + Side length^2)
Substituting the value:
Diagonal = √(34^2 + 34^2)
Diagonal = √(2,896 + 2,896)
Diagonal = √5,792
Diagonal = 76 inches
For the rectangular table:
Width = 29 1/3 inches
Length = 35 inches
The formula for the diagonal of a rectangle is given by:
Diagonal = √(Width^2 + Length^2)
Substituting the values:
Diagonal = √((29 1/3)^2 + 35^2)
Diagonal = √((29.33)^2 + 35^2)
Diagonal = √(861.0889 + 1225)
Diagonal = √2086.0889
Diagonal ≈ 45.68 inches
Now, let's determine which diagonal has a length that is an irrational number.
The diagonal length of the square table is 76 inches, which is a rational number because it can be expressed as a fraction.
The diagonal length of the rectangular table is approximately 45.68 inches, which is an irrational number. It cannot be expressed as a fraction and has infinite non-repeating decimal places.
Therefore, the rectangular table has a diagonal whose length is an irrational number, and the length of this diagonal is approximately 45.68 inches.