SOLUTION: In the diagram; DC is parallel to AB, and DA is perpendicular to AB. If DC = 1, DA = 4, AB = 10; and the area of quadrilateral APCD equals the area of triangle CPB, then what is th

Algebra ->  Finance -> SOLUTION: In the diagram; DC is parallel to AB, and DA is perpendicular to AB. If DC = 1, DA = 4, AB = 10; and the area of quadrilateral APCD equals the area of triangle CPB, then what is th      Log On


   

Question 1150430: In the diagram; DC is parallel to AB, and DA is perpendicular to AB. If DC = 1, DA = 4, AB = 10; and the area of quadrilateral APCD equals the area of triangle CPB, then what is the PB?
https://imgur.com/K8mlQTV
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Let the length to be found, PB, be x.

Then, since AB = 10, AP = 10-x.

The altitudes of the triangle and trapezoid are both DA = 4.

The areas of the trapezoid and triangle are the same:

%281%2F2%29%284%29%28%281%2B%2810-x%29%29%29+=+%281%2F2%29%284%29%28x%29
2%2811-x%29+=+2x
22-2x+=+2x
22+=+4x
x+=+5.5

ANSWER: PB = 5.5