Answer and show work for both a and b

C. H = 9 cm and B = 27 cm

Step-by-step explanation:

Topic: Geometry Perimiter

Topic 2: One unknown Equation

You have to be clear on the perimeter of a rectangle, the perimter of a geomestric figure it's defined by its contour lenght. In the case of a rectangle we have to do the sum its sides as you can see in the image.

Now you have to built a one unknown equation with the given information

So to calculate the perimeter of a rectangle you have

P = ∑ Li

it would make

P = h + b + h + b equals to P = 2h + 2b

But you know that b = 3h so replacing

P = 2h  + (2x(3h))

P = 2h + 6 h also you know the perimeter is 72 cm so P = 72 cm

72 cm = 8 h

now you have to find the value of h

h = 72/8 cm so h =   9 cm

Yeah we already know the height of the rectangle but we still missing the base, but you know the base is 3 times its heifght (b = 3h)

so replacing h by 9 we have that

b = 3 x (9 cm)

means b = 27 cm, so we have that the correct answer is C. h = 9 cm and b = 27 cm