A quilter wants to make the design shown at left using the Golden Ratio. Specifically, he wants the ratio of the triangle heights A : B and B: C to each equal 1.62. If the quilter makes the triangle height A 8 in, approximately how tall should he make triangle height C?

A. 3in

B. 4in

C. 5in

D. 6in

Answer: A. 3 inches

Step-by-step explanation:

According to the question,

The ratio of the height of triangle A and B is 1.62.

Let the height of A = 1.62 x and the height of B = x

Where x is any number.

But the height of A is 8,

⇒ 1.62 x = 8

⇒ x = 8/1.62

⇒ height of B = 4.93827160494

Again according to the question,

The ratio of height of triangle B and C is 1.62.

Thus, let the height of B = 1.62 y and the height of C = y

Where y is any number.

⇒ 1.62 y = 4.93827160494

⇒ y = 4.93827160494/1.62

⇒ y = 3.04831580552 ≈ 3

Thus, the height of C = 3 inches (approx)