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 the diagonals?
The difference in the length of the diagonals is:
9√2 - 8√2 = √2.
To find the difference in the length of the diagonals, we subtract the length of one diagonal from the other.
Given:
Length of one diagonal = 9√2 cm
Length of the other diagonal = 8√2 cm
Difference in the length of the diagonals = (Length of one diagonal) - (Length of the other diagonal)
= (9√2 cm) - (8√2 cm)
To subtract the diagonals, we can subtract the coefficients of √2.
= 9√2 - 8√2
Since the square root of 2 is the same in both terms, we can directly subtract the coefficients.
= (9 - 8)√2
= 1√2
Therefore, the difference in the length of the diagonals is 1√2 centimeters.
To find the difference in the length of the diagonals of the two tiles, we subtract the length of one diagonal from the length of the other diagonal.
Given:
Length of the first diagonal = 9√2 cm
Length of the second diagonal = 8√2 cm
Difference in diagonal lengths = Length of the second diagonal - Length of the first diagonal
= (8√2 cm) - (9√2 cm)
To subtract these two values, we need to ensure the units and the radical parts are the same.
Since both lengths have the same radical part (√2), we only need to consider the numerical coefficients.
8 - 9 = -1
Therefore, the difference in the length of the diagonals is -1√2 cm, or simply -√2 cm.