Aquilter 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

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)

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.