Answer:
The value of x = 13
The value of KN = 23.5
Step-by-step explanation:
Here are some of the characteristics of a rectangle.
- The diagonals of a rectangle are equal.
- The diagonals of a rectangle bisect each other.
Given the diagonals of a rectangle
KM = 4x-15
KL = 9x-80
We know that the diagonals of a rectangle are equal, so
KL=KM
9x-80=4x-15
9x-4x= -15+80
5x = 65
divide both sides by 5
5x/5 = 65/5
x = 13
Therefore, the value of x = 13
as
KM = 4x-15
so substitute x = 13
KM = 4(13) - 5 = 52 - 5 = 47
From the diagram, it is clear that N is the midpoint of the diagonal KM.
so
KN = 1/2 KM
substitute KM = 47
KN = 1/2 × 47
KN = 23.5
Therefore, the value of KN = 23.5
Summary:
The value of x = 13
The value of KN = 23.5
