Monday, June 13, 2016

Daily Regents: Right Triangle Altitude Theorem (January 2016)

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams next week. At least, that is the plan.

I had a question about this problem on the thread where I posted all the multiple-choice answers: http://mrburkemath.blogspot.com/2016/02/january-2016-new-york-geometry-common.html

Common Core Geometry, January 2016, Question 22

30. 2 In the diagram below, CD is the altitude drawn to the hypotenuse AB of right triangle ABC.
Which lengths would not produce an altitude that measures 6√2?

The Right Triangle Altitude Theorem tells us that (AD)(DB) = (CD)2
The square of the altitude is (6√2)(6√2) = (36)(2) = 72.
So which choice has lengths of AD and DB that have a product of something other than 72?

Careful! Two of the options give you AB instead of DB. Subtract AB - AD to get DB.

Look at the four choices:

  1. - 2 * 36 = 72. Not the answer
  2. - 3 * (24 - 3) = 3 * 21 = 63, not 72. This is the correct answer.
  3. - 6 * 12 = 72. Not the answer
  4. - 8 * (17 - 8) = 8 * 9 = 72. Not the answer.

The correct answer is choice (2).


Any questions?


If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.


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