Another painting has length : width ratio approximately equal to the golden ratio (1 + sqrt 5) : 2. Find the length of the painting if the width is 34 inches.
it’s 55
To find the length of the painting, we will use the given information about the length-to-width ratio and the width of the painting.
The golden ratio is approximately equal to 1.61803398875. It can be represented mathematically as (1 + sqrt(5)) / 2.
We are given the width of the painting as 34 inches. Let's assume the length of the painting is L inches.
According to the given ratio, we can set up the following equation:
L / 34 = (1 + sqrt(5)) / 2
To find L, we can multiply both sides of the equation by 34:
L = 34 * (1 + sqrt(5)) / 2
Now, we can simplify the expression:
L = 17 * (1 + sqrt(5))
Multiplying 17 by (1 + sqrt(5)), we get:
L ≈ 29.2426406871
Therefore, the length of the painting is approximately 29.24 inches.
(1+sqrt 5) (34)
= 34 + 34 (2.236)
= 110