Question

Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 1, 1. Q is at 8, 1. R is at 8, 5. S is at 1, 5. Rectangle JKLM with vertices J at 4, 1. K is at 8, 1. L is at 8, 4. M is at 4, 4. Which statement is correct? The two tiles are not similar because segment SP is to segment SR is 4:7 and segment MJ is to segment ML is 1:3. The two tiles are similar because segment PQ is to segment QR is 4:3 and segment JK is to segment KL is also 4:3. The two tiles are similar because segment SR is to segment ML is 7:4 and segment PQ is to segment JK is also 7:4. The two tiles are not similar because segment PQ is to segment QR is 7:4 and segment JK is to segment KL is 4:3.

Answer 1

From the given figure,
the length of segment SP is 5 - 1 = 4,
the length of segment SR is 8 - 1 = 7,
the length of segment QR is 5 - 1 = 4,
the length of segment PQ is 8 - 1 = 7.

The length of segment MJ is 4 - 1 = 3,
the length of segment ML is 8 - 4 = 4
the length of segment KL is 4 - 1 = 3
the length of segment JK is 8 - 4 = 4

segment SP to segment SR is 4 : 7
segment MJ to segment ML is 3 : 4

segment PQ to segment QR is 7 : 4
segment JK to segment KL is 4 : 3

Because the ratio of any corresponding segments of the two rectangles to another segment is not equal, the two rectangles are not similar.

Therefore, the correct statement is "The two tiles are not similar because segment PQ is to segment QR is 7:4 and segment JK is to segment KL is 4:3"