Question

1. a painting measures 15 cm long by 24 cm high. you buy two posters, each showing an enlargement of the painting. the first poster measures 45 cm long by 72 cm high. the second poster measures 91.5 cm long by 136 cm high. which of the following is true? (hint: to be an accurate representation of the painting, would the poster be similar to the painting?)

Explanation:

Step1: Calculate the scale factor for the first poster

The painting is \(15\) cm long and \(24\) cm high. The first poster is \(45\) cm long and \(72\) cm high.
For the length: \(\frac{45}{15}=3\). For the height: \(\frac{72}{24} = 3\). Since the ratios of length and height are equal, the first poster is an accurate representation (similar to the painting as the ratios of corresponding sides are equal).

Step2: Calculate the scale factor for the second poster

The second poster is \(91.5\) cm long and \(136\) cm high.
For the length: \(\frac{91.5}{15}=6.1\). For the height: \(\frac{136}{24}=\frac{17}{3}\approx5.67\). Since \(6.1
eq\frac{17}{3}\), the second poster is not an accurate representation (ratios of corresponding sides are not equal).

Answer:

The first poster is an accurate representation of the painting, but the second poster is not an accurate representation.