Question

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 97.5 cm long by 156 cm high. Which of the following is true? (Hint: To be an accurate representation of the painting, would the the poster be similar to the painting?)

Answer 1

To determine if the posters are accurate representations of the painting, we need to check the aspect ratios (the ratio of height to length) of the painting and the posters.

1. Aspect ratio of the painting:

   • Length = 15 cm
   • Height = 24 cm
   • Aspect ratio = Height/Length = 24/15 = 8/5

2. Aspect ratio of the first poster:

   • Length = 45 cm
   • Height = 72 cm
   • Aspect ratio = Height/Length = 72/45 = 8/5

3. Aspect ratio of the second poster:

   • Length = 97.5 cm
   • Height = 156 cm
   • Aspect ratio = Height/Length = 156/97.5

   To simplify this fraction, we can calculate:

   \[ \frac{156}{97.5} = \frac{156 \times 2}{97.5 \times 2} = \frac{312}{195} = \frac{312 \div 39}{195 \div 39} = \frac{8}{5} \]

Since both posters have the same aspect ratio of \( \frac{8}{5} \), which is the same as the painting's aspect ratio, this means both posters are indeed accurate representations of the painting and are similar to it.

Conclusion: Both posters are similar to the painting.