What is the perimeter of this figure?

66.56cm =  perimeter

Step-by-step explanation:

First find the easy part (the rectangle)

10+10+17+17=54

subtract the part that is not really there (dashes)

54-8=46

Add the height of the circular part

46+8=54

Find the circumference of a circle with a radius of 8

2(8)(3.14)=50.24

Divide by 4 (the circumference is only 1/4 of the the actual circle in this problem)

50.24/4=12.56

Add all of it together

12.56+54=66.56

what are you trying to solve here

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240