Question

A golden rectangle is 32cm long.The ratio of length to width is (1 + square root of 5) :2. What is the width of the rectangle in simplest radical form?

Answer 1

Width = 16(√5) - 1

Explanation:

We are told that the golden rectangle is 32 cm long.

Thus, length = 32 cm

We are also told that the ratio of the length to the width is; (1 + √5):2

Thus;

If a length of (1 + √5) yields a width of 2

Then, a length of 32 cm would yield a width of; (32 x 2)/(1 + √5)

So corresponding width = 64/(1 + √5)

We want to reduce this width to it's simplest radical form which means the denominator should have no square root.

Thus, let's multiply top and bottom by (1 - √5);

Width = 64 x (1 - √5)/[(1 + √5) x (1 - √5)]

Width = 64(1 - √5)/(1 - 5)

Width = 64(1 - √5)/(-4)

Width = -16(1 - √5)

Width = 16(√5 - 1)

Width = 16√5 - 1