Question

Todd placed 32 square tiles along the edge of his wooden dining room table, as shown below.

Todd wants to paint a design on the wood along the diagonal shown. If each tile is 13 centimeters on each side, what is the length of the diagonal shown?
A. 182 centimeters
B. 169 centimeters
C. 130 centimeters
D. 91 centimeters

Answer 1

130 centimeters

Explanation:

We need to use the Pythagorean Theorem to solve this problem. We know that each tile is 13 centimeters on each side. So in the vertical side of the triangle we see 6 tiles following the sequence white-blue-white-blue-white-blue. Therefore, this side of the triangle is 6 x 13 = 78 cm. On the other hand, in the horizontal side of the triangle we see 8 tiles following the sequence blue-white-blue-white-blue-white-blue-white. Therefore, this side of the triangle is 8 x 13 = 104 cm. Finally, by applying Pythagorean Theorem we have:

`L=√(78^2+104^2)=\boxed{130 \ cm}`

Answer 2

The correct answer option is C. 130 centimeters.

Explanation:

Since each tile is 13 centimeters on each side and considering the diagonal shown in the picture, it makes a right angled triangle.

Now this right angled triangle has 6 tiles on one side and 8 tiles on the other side. Multiplying the number of tiles by 13 to find the side lengths and then using the Pythagoras Theorem to find the length of the diagonal.

6 × 13 = 78

8 × 13 = 104

Length of diagonal =
`√((78)^2+(104)^2) =√(16900) =130`