ABCD is a parallelogram. AD = 12 cm.
DC = 9 cm.
The perpendicular distance of
from CD is 8 cm.
What is the perpendicular distance of AD from BC?

9514 1404 393

  6 cm

Step-by-step explanation:

The area of the parallelogram is the same, either way you figure it.

  A = bh

  A = CD(length ⊥ to CD)

  A = (9 cm)(8 cm) = 72 cm²

__

  A = AD(length ⊥ AD)

  72 cm² = (12 cm)(length ⊥ AD)

  (length ⊥ AD) = (72 cm²)/(12 cm) = 6 cm

The perpendicular distance of AD from BC is 6 cm.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!