Question

Points A, B, C, D, and O have coordinates (0, 3), (4, 4), (4, y), (4, 0), and (0, 0), respectively. The area of ACDO is 5 times greater than the area of ABDO. Find y. Answer:

Answer 1

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

$A_{ABDO}=\dfrac{AO+BD}{2}\cdot OD=\dfrac{3+4}{2}\cdot 4=14\ un^2.$

Since the area of ACDO is 5 times greater than the area of ABDO, then

$A_{ACDO}=5\cdot 14=70\ un^2.$

Now

$A_{ACDO}=\dfrac{AO+CD}{2}\cdot OD=\dfrac{3+CD}{2}\cdot 4=6+2CD.$

Hence

$6+2CD=70,\\ \\2CD=70-6=64,\\ \\CD=32\ un.$

This means that y=32.