The tiles in a store are being compared. The diagonal of one tile is 9√2 centimeters, and the other tile is 8√2 centimeters. What is the difference in the length of diagonals?
The difference is __ centimeters.
The difference in the length of diagonals is (9√2 - 8√2) centimeters.
Simplifying the expression inside the parentheses, we get:
9√2 - 8√2 = √2
Therefore, the difference in the length of diagonals is √2 centimeters.
To find the difference in the length of the diagonals, we need to subtract the length of one diagonal from the other.
Let's call the length of the first diagonal "d1" and the length of the second diagonal "d2".
Given that d1 = 9√2 centimeters and d2 = 8√2 centimeters, the difference can be calculated as follows:
Difference = d1 - d2
Substituting the values, we have:
Difference = 9√2 - 8√2
To subtract these two values, we need to have the same radical. Since both terms have √2, we can perform the subtraction:
Difference = (9 - 8)√2
Simplifying further,
Difference = 1√2
Since we cannot leave the answer in terms of the radical, we need to simplify √2, which is approximately 1.414.
Difference = 1√2 ≈ 1.414
Therefore, the difference in the length of diagonals is approximately 1.414 centimeters.
To find the difference in the length of the diagonals, subtract the length of one diagonal from the length of the other diagonal.
Given:
Length of diagonal of one tile = 9√2 centimeters
Length of diagonal of the other tile = 8√2 centimeters
Difference in the length of diagonals = (Length of diagonal of one tile) - (Length of diagonal of the other tile)
= 9√2 - 8√2
First, let's simplify the expression by combining like terms:
Difference in the length of diagonals = (9 - 8)√2
= 1√2
Since the square root of 2 cannot be simplified further, the difference in the length of diagonals is 1√2 centimeters.