Rectangle A is similar to rectangle B. Rectangle A has side lengths of 6 and 12. Rectangle B has a side length of 18. What are the possible values for the length of the other side of rectangle B?
Question
Rectangle A is similar to rectangle B. Rectangle A has side lengths of 6 and 12. Rectangle B has a side length of 18. What are the possible values for the length of the other side of rectangle B?
Solution
Rectangle A and Rectangle B are similar, which means their sides are proportional.
The sides of Rectangle A are 6 and 12, so the ratio of the sides is 6:12 or 1:2.
Rectangle B has one side that is 18. To find the length of the other side, we can set up a proportion using the ratio from Rectangle A.
If we let x be the unknown side of Rectangle B, we can set up the following proportions:
1:2 = 18:x or 1:2 = x:18
Solving the first proportion for x gives x = 36. This means that if the 18 side of Rectangle B corresponds to the 6 side of Rectangle A, the other side of Rectangle B is 36.
Solving the second proportion for x gives x = 9. This means that if the 18 side of Rectangle B corresponds to the 12 side of Rectangle A, the other side of Rectangle B is 9.
So, the possible values for the length of the other side of Rectangle B are 36 and 9.
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