Question 1150430
<br>
Let the length to be found, PB, be x.<br>
Then, since AB = 10, AP = 10-x.<br>
The altitudes of the triangle and trapezoid are both DA = 4.<br>
The areas of the trapezoid and triangle are the same:<br>
{{{(1/2)(4)((1+(10-x))) = (1/2)(4)(x)}}}
{{{2(11-x) = 2x}}}
{{{22-2x = 2x}}}
{{{22 = 4x}}}
{{{x = 5.5}}}<br>
ANSWER: PB = 5.5<br>