The larger square garden at volterra hall has sides twice as long as the smaller square garden. together the gardens cover 18,000 square feet. find the dimensions of each garden.

We will call:
: The larger square garden.
: The smaller square garden.

Given that both of then have square areas, then:



Being the side of the larger garden and the side of the smaller garden as shown in the figure.

The larger square garden at Volterra Hall has sides twice as long as the smaller square garden, thus:



Together the gardens cover 18,000 square feet, so:


Then:








Therefore:
Each side of the larger square garden is and each side of the smaller one is each. These are the dimensions.

Answer: 10pi

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

Ithink the versus years?