The length of a Rectangle is five less than twice its width the perimeter is 26 m find the dimensions of the rectangle

L = 7 m

W = 6 m

Step-by-step explanation:

P = 2L + 2W

26 = 2(2W - 5) + 2W

26 = 4W - 10 + 2W

26 = 6W - 10

+10.         +10

36 = 6W

divide both sides by 6

36/6 = W

6 = W

L = 2(6) - 5

L =12 - 5 = 7

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.