Question

Please help!! Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Which statement is correct?
a. The two tiles are not similar because SP:SR is 5 : 1 and MJ:ML is 2 : 3.
b. The two tiles are similar because PQ:QR is 1 : 3 and JK:KL is also 1 : 3.
c. The two tiles are similar because SR:SP is 3 : 2 and ML:MJ is also 3 : 2.
d. The two tiles are not similar because PQ:QR is 1 : 6 and JK:KL is 1 : 3.

Answer 1

Answer: Statement B is correct; the two tiles are similar because PQ:QR is 1:3 and JK:KL is also 1:3

Step-by-step explanation: The two tiles as shown in the diagram has their dimensions given according to their position on the Cartesian plane. Tile SRQP has its width at coordinates (2,2) and (4,2) which means the width spans from 2 cm to 4 cm on the x-axis, that is a length of 4 minus 2 which is 2 cm. Similarly the length is at coordinates (2,2) to (2,8) which means the length spans from 2 cm to 8 cm on the y-axis, that is a length  of 8 minus 2 which is 6 cm. Therefore the dimensions of the first tile is 6 cm by 2 cm.

Similarly, we can derive the length and width of the smaller tile MLKJ, by applying the same procedure and what we would have is a tile measuring 3 cm by 1 cm.

The ratio of tile SRQP can be derived as

Ratio = 2 : 6

Ratio = 1 : 3

Also the ratio of the tile MLKJ can be derived as

Ratio = 1 : 3

Having calculated the ratio 1 : 3 for both tiles, then we can safely conclude that both are similar.