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

y=32.

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)=(AO+BD)/(2)\cdot OD=(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)=(AO+CD)/(2)\cdot OD=(3+CD)/(2)\cdot 4=6+2CD.`

Hence

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

This means that y=32.