Question

A golden rectangle is a rectangle whose length is approximately 1.6 times its width.The early Greeks thought that a rectangle with these dimensions was the most pleasing to the eye and examples of the golden rectangle are found in many early works of art. For​ example, the Parthenon in Athens contains many examples of golden rectangles. Mike Hallahan would like to plant a rectangular garden in the shape of a golden rectangle. If he has 208 feet of fencing​ available, find the dimensions of the garden.

Answer 1

Answer:

$l = 64, w=40$

Step-by-step explanation:

length = 1.6 times width, Thus

$l = 1.6w$

Mike has 208 feet of fencing which is the distance around, this is also known as the perimeter

the perimeter of a rectangle is $2(l+w)$

$2(l+w) = 208$

and we know $l = 1.6w$ from earlier, so we plug it in for l

$2((1.6w) + w) = 208\\2(2.6w) = 208\\2.6w = 104\\w = 40$

we now have w and to find l we use $l = 1.6w$

$l = 1.6(40)\\l = 64$

These are the dimensions

$l = 64, w=40$