Todd placed 32 square tiles along the edge of his wooden dining room table, as shown below.
Note: Figure is not drawn to scale.
Todd wants to paint a design on the wood along the diagonal shown. If each tile is 15 centimeters on each side, what is the length of the diagonal shown?
A. 195 centimeters
B. 105 centimeters
C. 150 centimeters
D. 210 centimeters
To find the length of the diagonal, we can use the Pythagorean theorem, which states that a^2 + b^2 = c^2, where c is the length of the diagonal and a and b are the sides of the right triangle formed by the diagonal and the sides of the table.
Since each side of the square tile is 15 centimeters, the sides of the right triangle are 30 centimeters and 30 centimeters (2 tiles along the side of the table).
So, a = 30 cm and b = 30 cm.
Plugging these values into the Pythagorean theorem:
30^2 + 30^2 = c^2
900 + 900 = c^2
1800 = c^2
c = √1800
c ≈ 42.42
Therefore, the length of the diagonal shown is approximately 42.42 centimeters. None of the options provided match this answer, so it seems that the correct answer is missing.