An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 13 more than three times the length of the bottom of the triangle. The last side is 14 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.

Step-by-step explanation:

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Step-by-step explanation:

P = 4x + 24

Step-by-step explanation:

Sides of the triangle:

bottom = x

side1 = 2x + 13

side2 = x + 11

Perimeter is the sum of side lengths:

P = x + 2x + 13 + x + 11 = 4x + 24

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.

no problobm

step-by-step explanation: