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

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(13215) (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:

ANSWER: PB = 5.5

RELATED QUESTIONS
In the diagram below, AB, EF and DC are perpendicular to BC. AEC and BED are straight... (answered by ankor@dixie-net.com)

In a diagram of a large quadrilateral, AD is parallel to BC, BD is perpendicular to DC,... (answered by venugopalramana,keigan)

In the diagram below AB is parallel to DE AB=20 inches and BC=15inches what is the... (answered by ikleyn)

Quadrilateral ABCD is an isosceles trapezoid with AB parallel to DC, AC=DC, and AD=BC. If (answered by greenestamps)

In parallelogram ABCD AB parallel to DC and area of parallelogram is 280 square... (answered by ikleyn)

If AB is parallel to DC in a quadrilateral what could it... (answered by jim_thompson5910)

1.M is the mid-point of a line segment AB;AXB and MYB are equilateral triangles on... (answered by KMST)

ABCD is a trapezium in which AB is parallel to DC and ABC=90 (a)Given that AB=(2x-1)cm... (answered by josgarithmetic)

A lecture theatre in the shape of a prism has a height of 9 metres. The floor of the... (answered by greenestamps)