Answer:
y=32.
Step-by-step explanation:
Plot points A, B, D and O on the coordinate plane. Point C will lie on the vertical line BD. Quadrilatrals ACDO and ABDO are both trapezoids.
The are of the trapezoid ABDO is
[tex]A_{ABDO}=\dfrac{AO+BD}{2}\cdot OD=\dfrac{3+4}{2}\cdot 4=14\ un^2.[/tex]
Since the area of ACDO is 5 times greater than the area of ABDO, then
[tex]A_{ACDO}=5\cdot 14=70\ un^2.[/tex]
Now
[tex]A_{ACDO}=\dfrac{AO+CD}{2}\cdot OD=\dfrac{3+CD}{2}\cdot 4=6+2CD.[/tex]
Hence
[tex]6+2CD=70,\\ \\2CD=70-6=64,\\ \\CD=32\ un.[/tex]
This means that y=32.
