Question

The Golden Ratio appears in the design of the Greek Parthenon because the width and height of the façade are related by the equation $\frac{W+H}{W} = \frac{W}{H}$. If the height of a model of the Parthenon is 16 inches, what is its width? Round your answer to the nearest tenth.

Answer 1

Answer:

25.9 in

Step-by-step explanation:

Width and height relation equation:

• (W+H)/W= W/H

And also given,

• H=16 in

We need to find the value of W

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Plug in the value of H, the equation becomes:

• (W+16)/W=W/16

Cross- multiplication:

• 16(W+16)=W²
• W² - 16W - 256=0

Solving the quadratic equation:

• W= (-b±√b²-4ac)/2a
• W= (16±√1280)/2
• W= −9.889  this root is discarded as negative value
• W= 25.889 ≈ 25.9 in rounded to nearest tenth

Answer is  25.9 in