The perimeter of the rectangle is 28 units.
what is the value of w?

5

Step-by-step explanation:

Since this is a rectangle, opposite sides are congruent.

That is, the perimeter in terms of w is:

(2w-1)+(2w-1)+(w)+(w)

or

2(2w-1)+2(w)

We can simplify this.

Distribute:

4w-2+2w

Combine like terms:

6w-2

We are given that the perimeter, 6w-2, is 28.

So we can write an equation for this:

6w-2=28

Add 2 on both sides:

6w   =30

Divide both sides by 6:

w   =30/6

Simplify:

w   =5

w is 5

Check if w=5, then 2w-1=2(5)-1=10-1=9.

Does 5+5+9+9 equal 28? Yep it does 10+18=28.

w=5

Step-by-step explanation:

To find the perimeter of the rectangle

P = 2(l+w)

where w is the width and l is the length

Our dimensions are w and 2w-1 and the perimeter is 28

Substituting into the equation

28 = 2(2w-1 +w)

Combining like terms

28 = 2(3w-1)

Divide each side by 2

28/2 = 2(3w-1)/2

14 = 3w-1

Add 1 to each side

14+1 = 3w-1+1

15 = 3w

Divide each side by 3

15/3 =3w/3

5 =w

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.

cosine

step-by-step explanation: