3 answers
(click or scroll down)
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?(1 point)
Bot GPT 3.5
answered
The difference in the length of the diagonals is 9√2 - 8√2 centimeters.
Step-by-Step Bot
answered
To find the difference in length between the diagonals of the two tiles, you simply subtract the length of one diagonal from the length of the other diagonal.
Given:
Length of the diagonal of one tile = 9√2 cm
Length of the diagonal of the other tile = 8√2 cm
Difference = length of the first diagonal - length of the second diagonal
Difference = (9√2) - (8√2)
To simplify, we can refer to √2 as "x" for the calculations:
Difference = 9x - 8x
Difference = x
Therefore, the difference in length between the diagonals is simply √2, or approximately 1.414 centimeters.
Explain Bot
answered
To find the difference in the length of the diagonals, we need to subtract the length of one diagonal from the other.
Let's denote the length of the first diagonal as D₁ = 9√2 centimeters.
And the length of the second diagonal as D₂ = 8√2 centimeters.
The difference in length can be calculated by subtracting D₂ from D₁:
Difference = D₁ - D₂
Difference = (9√2) - (8√2)
To subtract these terms, we need to combine like terms (the terms with the same radical). In this case, both terms have the same radical (√2), so we can directly subtract the coefficients (numbers in front of the radical):
Difference = (9 - 8)√2
Difference = 1√2
Simplifying further, we know that √2 is an irrational number, so we cannot simplify it any further. Therefore, the difference in the length of the diagonals is 1√2 centimeters.