Question

1. the parallelograms below are similar. what is the value of x? 18 ft, 9 ft, x ft, 12 ft

Explanation:

Step1: Set up proportion for similar figures

Since the parallelograms are similar, their corresponding sides are proportional. So, $\frac{9}{12}=\frac{18}{x}$ (or equivalently, $\frac{9}{18}=\frac{12}{x}$? Wait, no, let's check the sides. The first parallelogram has sides 9 ft and 18 ft, the second has 12 ft and x ft. So corresponding sides: 9 corresponds to 12, 18 corresponds to x. So proportion is $\frac{9}{12}=\frac{18}{x}$? Wait, no, similar figures have corresponding sides in proportion. So the ratio of the first side (9) to the second side (12) should equal the ratio of the first base (18) to the second base (x). So $\frac{9}{12}=\frac{18}{x}$? Wait, no, maybe $\frac{9}{18}=\frac{12}{x}$? Wait, let's think again. The first parallelogram: side length 9, base 18. The second: side length 12, base x. So the ratio of side to base in first is 9/18, and in second is 12/x. Since they are similar, these ratios are equal. So $\frac{9}{18}=\frac{12}{x}$? Wait, no, maybe the other way. Wait, similar figures: corresponding sides are proportional. So the side of the first (9) corresponds to the side of the second (12), and the base of the first (18) corresponds to the base of the second (x). So the proportion is $\frac{9}{12}=\frac{18}{x}$. Let's solve that. Cross-multiplying: 9x = 1218. 1218 = 216. Then x = 216/9 = 24. Wait, or maybe I mixed up. Wait, let's check the ratio of scaling. From 9 to 12: the scale factor is 12/9 = 4/3. So the base should be 18*(4/3) = 24. Yes, that makes sense. So step by step:

Step1: Identify corresponding sides

The sides of the first parallelogram are 9 ft (side) and 18 ft (base). The second has 12 ft (side) and x ft (base). Since similar, the ratio of side to base (or side to side, base to base) is equal. So ratio of side: 9/12 = 3/4? Wait, no, 9 to 12 is 3/4, so 18 to x should also be 3/4? Wait, no, 9/12 = 3/4, so 18/x = 3/4? Then x = 18*(4/3) = 24. Yes, that's correct.

Step2: Set up the proportion

Let’s set up the proportion using corresponding sides. The ratio of the side of the first parallelogram (9 ft) to the side of the second (12 ft) is equal to the ratio of the base of the first (18 ft) to the base of the second (x ft). So:
$$\frac{9}{12} = \frac{18}{x}$$

Step3: Cross - multiply to solve for x

Cross - multiplying gives:
$$9x = 12\times18$$
First, calculate $12\times18 = 216$. Then:
$$9x = 216$$
Divide both sides by 9:
$$x=\frac{216}{9}=24$$

Answer:

24