The length of the diagonal AC is equal to the length of the diagonal BD,
which is 8×10 - 32 = 48.
Response:
Which properties of a rectangle is used to find the length the diagonal AC?
The given parameters are;
The diagonals of the rectangle are AC and BD
The point of intersection of the rectangle = Point E
AE = 2·x + 4
BD = 8·x - 32
Required:
The length of AC
Solution:
The diagonals of a rectangle bisect each other and have equal length.
Therefore;
AE = [tex]\mathbf{\frac{1}{2}}[/tex] × BD
Which gives;
[tex]2 \cdot x + 4 = \mathbf{\dfrac{1}{2} \times \left(8 \cdot x - 32\right)}[/tex]
2·x + 4 = 4·x - 16
4·x - 2·x = 4 + 16 = 20
2·x = 20
[tex]x = \dfrac{20}{2} = 10[/tex]
x = 10
AC = 2 × AE
Which gives;
AC = 2 × (2·x + 4) = 4·x + 8
- The length of AC = 4 × 10 + 8 = 48
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