Question

a golden rectangle is to be constructed such that the shortest side is 23ft long. How long is the other side? round to the nearest tenth of a foot

Answer 1

37.2

Step-by-step explanation:

A golden rectangle is a rectangle that satisfies the following proportion:

`(a+b)/(a)=(a)/(b)`

Where a is the shortest side and (a+b) is the length of the other side. So, we can replace a by 23 and calculate b as:

`(23+b)/(23)=(23)/(b)`

Applying cross-multiplication, we get:

`\begin{gathered} (23+b)\cdot b=23\cdot23 \\ 23b+b^2=529 \\ b^2+23b-529=0 \end{gathered}`

Therefore, we can find the solutions to the quadratic function as:

`\begin{gathered} b=\frac{-23\pm\sqrt[]{23^2-(4\cdot1\cdot(-529))}_{}}{2\cdot1} \\ b=14.215 \\ or \\ b=-37.215 \end{gathered}`

Since -37.215 doesn't have any sense here, the value of b is 14.215

It means that the length of the longest side is:

a + b = 23 + 14.215 = 37.215

So, the answer is 37.2