2 similar quadrilaterals are shown below. Line ML equals 12cm. The ratio of the lengths of the corresponding sides MN and ST is 2:3, respectively. What is the measure of RS?

I am confused on how to solve for line RS with the ratio and with 12.

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To solve for the measure of RS, we need to use the given ratio and information about the lengths of other sides. Here's how you can approach the problem step-by-step:

1. Identify the similar quadrilaterals and corresponding sides: In this case, let's assume quadrilateral MNLK and quadrilateral STQR are similar. The given information tells us that MN is corresponding to ST and line ML equals 12cm.

2. Use the ratio to find the length of ST: Since the ratio of the lengths of MN to ST is 2:3, we know that MN is two-thirds the length of ST. Therefore, if MN = 12cm, ST would be (12cm * 3/2) = 18cm.

3. Determine the length of SR: Since quadrilateral MNLK and quadrilateral STQR are similar, the corresponding sides have proportional lengths. Therefore, if line ML equals 12cm in quadrilateral MNLK, and STQR is similar to MNLK, the ratio of the lengths ML:RS will also be 2:3.

4. Set up a proportion: We can set up the proportion using the given ratio and the lengths of the corresponding sides. The proportion is as follows:

ML / RS = MN / ST

Plugging in the values we know: 12cm / RS = 12cm / 18cm

5. Solve for RS: We can cross-multiply the proportion and solve for RS:

12cm * 18cm = 12cm * RS

216cm^2 = 12cm * RS

RS = 216cm^2 / 12cm

RS = 18cm

Therefore, the measure of RS is 18cm.