Answer:
56 cm
Step-by-step explanation:
The ratio of the lengths of the pieces is 3:4.
The longer piece is 32 cm.
We set up a proportion to find the length of the smaller piece.
Let the length of the smaller piece be x.
3 is to 4 as x is to 32
3/4 = x/32
4x = 3 * 32
4x = 96
x = 24
The smaller piece is 24 cm.
24 cm + 32 cm = 56 cm
The missing coordinates of the parallelogram is (m + h, n).
Solution:
Diagonals of the parallelogram bisect each other.
Solve using mid-point formula:

Here 


<u>To find the missing coordinate:</u>
Let the missing coordinates by x and y.
Here 



Now equate the x-coordinate.

Multiply by 2 on both sides of the equation, we get
m + h = x
x = m + h
Now equate the y-coordinate.

Multiply by 2 on both sides of the equation, we get
n = y
y = n
Hence the missing coordinates of the parallelogram is (m + h, n).
We are given that the angle a is the right angle. So let
us work from this.
ab = 12 (the vertical side of the triangle)
bc = 13 (which if drawn can be clearly observed to be the
hypotenuse) = the side opposite to angle a
ca = 5 (the horizontal side of the triangle)
Since we are to find for the cosine ratio of angle c or
angle θ, therefore:
cos θ = adjacent side / hypotenuse
cos θ = ca / bc
cos θ = 5 / 13
Check out the attached image below for the illustration
of the triangle.
I don't understand, could you explain further?