Question

1. rectangles abcd and pqrs are similar.

ac = 4 cm
cd = 9 cm
pq = 12 cm

Explanation:

Step1: Identify the ratio of corresponding sides

Since rectangles \(ABCD\) and \(PQRS\) are similar, the ratios of corresponding sides are equal. Let's find the ratio of the sides \(PQ\) and \(AC\). The length of \(AC = 4\space cm\) and \(PQ = 12\space cm\), so the scale factor \(k=\frac{PQ}{AC}=\frac{12}{4} = 3\).

Step2: Find the length of \(PS\)

The side \(CD = 9\space cm\) in rectangle \(ABCD\) corresponds to side \(PS\) in rectangle \(PQRS\). Using the scale factor \(k = 3\), we can find \(PS\) by multiplying the length of \(CD\) by the scale factor. So \(PS=CD\times k = 9\times3 = 27\space cm\).

Answer:

The length of \(PS\) is \(27\space cm\).