Question 1064005
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Interesting problem; and interesting responses....<br>
Finding the area of the triangle using the coordinates of A, B, C, and D in the formula for the area of a triangle (one-half base times height) is not a particularly good way.  For one thing the coordinates of D are only given approximately; for another thing, you end up doing ugly arithmetic with decimal approximations of the lengths of the base and height.<br>
On the other hand, since the problem asks to find lengths rounded to the nearest tenth, you can get the answer that way.<br>
But, wait -- using either that approximate method or any of at least two exact methods, the correct answer of (exactly) 15.5 is not one of the answer choices.  So here the problem is faulty....<br>
Finally, as a note regarding the response from the other tutor, you should never take it as the gospel truth when someone says that a particular method is the best way to work a problem.  Enclosing the triangle in a rectangle and finding the area of the given triangle as the area of the rectangle minus the area of the three small triangles is A good way to solve the problem; but there are other equally good ways.<br>
The length of the base AB is found simply using the Pythagorean Theorem -- although again, given the set of answer choices and the instruction to find the length to the nearest tenth, 8.1 is the obvious answer.<br>
And, finally, only one of the answer choices is reasonable for the length of altitude AD.<br>