Math Question on ACT June 2013

Test Preparation
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<p>I'm looking over my math section of my June 2013 ACT, and there are a couple of questions that I missed and can't seem to figure out how to solve them! If anyone could help explain this to me, it would be great! Thanks a lot!</p>

<h1>52 Which of the following sets of 3 lengths, in decimeters, are the side lengths of an obtuse triangle?</h1>

<p>F. {4,4,5}
G. {5,12,13}
H. {6,8,10}
J. {7,10,12}
K. {8,11,16}</p>

<p>...The answer is K...I understand why F, G, and H are not the answers. F is a 45-45 triangle and G & H are Pythagorean triples of a right triangle. I don't know why J is not the answer or why K is the answer....</p>

<h1>42 (has a picture but I'm just gonna write the question only and hope someone remembers it from the test) In the figure below, X and Z are on line m and, and Y is on line l. The exterior angle to triangleXYZ at Z measures 160 degrees. One of the following statements gives sufficient additional information to find the measure of <b. Which one?</h1>

<p>F. Line l is parallel to line m.
G. The measure of <d is 130 degrees.
H. The measure of <c is equal to the measure of <f.
J. The measure of <a is greater than the measure of <c.
K. The sum of the measurements of <b, <e, and <f is 180 degrees.</p>

<p>...Answer is G</p>

2

<p>1) - A triangle given sides a, b, and c is an obtuse triangle if the sides satisfies the inequalities a + b > c and a^2 + b^2 < c^2. This makes sense as for the triangle to be an obtuse triangle, the longest side needs to be much longer than the sums of the squares of the lengths of the other sides, since equal to is a right triangle, but for a triangle to be a triangle, the two short sides together must be longer than the longest side, otherwise we would not have a closed figure.</p>

<p>2) Can’t help ya’ there without the picture. Sorry about that.</p>

3

<p>thank you darksaber21!</p>