A golden rectangle has side lengths in the ratio of about 1 to 1.62. To the nearest tenth, what is length of the shorter side of a golden rectangle with a longer side length of 40 inches?

Respuesta :

Answer: The  length of the shorter side of a golden rectangle is about 24.7 inches.

Step-by-step explanation:

Given : A golden rectangle has side lengths in the ratio of about 1 to 1.62.

Since 1.62 > 1 , so

[tex]\dfrac{\text{Length of shorter side}}{\text{Length of longer side}}=\dfrac{1}{1.62}[/tex]

If the length of the longer side is 40 inches , then we have

[tex]\dfrac{\text{Length of shorter side}}{\text{40 inches}}=\dfrac{1}{1.62}\\\\ \Rightarrow\ \text{Length of shorter side}=\dfrac{1}{1.62}\times \text{40 inches}\\\\ \Rightarrow\ \text{Length of shorter side}=24.6913580247\approx24.7\text{ inches}[/tex]

Hence, the  length of the shorter side of a golden rectangle is about 24.7 inches.