Question

1. if the trapezoids shown are similar to each other, what is length of side x? trapezoid images with 3 cm, 4.5 cm, 1.8 cm, x options: 2.4, 3.4, 2.7, 1.8

Explanation:

Step1: Recall similarity ratio

For similar figures, the ratios of corresponding sides are equal. Let the first trapezoid have sides \( 4.5 \, \text{cm} \) (base) and \( 3 \, \text{cm} \) (height), and the second have base \( x \) and height \( 1.8 \, \text{cm} \). So, \( \frac{4.5}{x} = \frac{3}{1.8} \).

Step2: Solve for \( x \)

Cross - multiply: \( 3x = 4.5\times1.8 \). Calculate \( 4.5\times1.8 = 8.1 \). Then, \( x=\frac{8.1}{3}=2.7 \).

Answer:

2.7