Question 1181240
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A very fancy solution indeed from the other tutor....<br>
But that solution method makes a "first class" geometry problem out of a relatively simple algebraic one.<br>
Draw a sketch with the vertical edge of the right trapezoid at the left and the longer base at the bottom; let h be the height of the trapezoid.<br>
Then the slope of the shorter diagonal is x/8, and the slope of the longer diagonal is -x/18.<br>
The diagonals are perpendicular, so<br>
{{{(x/8)(-x/18)=-1}}}
{{{-x^2/144=-1}}}
{{{x^2=144}}}
{{{x = 12}}}<br>
The height of the trapezoid is 12; its area is<br>
{{{12((8+18)/2)=12(13)=156}}}<br>
ANSWER: 156<br>