<p>Note: Figure not drawn to scale</p>
<p>In the figure below, if the legs of triangle ABC are parallel to the axes, what could be the lengths of the sides of triangle ABC?</p>
<p>a) 2, 5 and sqrt 29
b)2, 5, 7
c)3, 3, and 3sqrt2
d)3, 4,5
e)4,5, and sqrt 41</p>
<p>Please show the steps.
Thanks in advance</p>
<p>Another question <a href="http://img30.imageshack.us/img30/1378/captureavt.jpg%5B/url%5D">http://img30.imageshack.us/img30/1378/captureavt.jpg</a></p>
<p>BC:AC = 10:4 by similar triangles. Therefore a).</p>
<p>1)The line AB pass O so its equation must be y=ax. While B(4;10) -> AB equation: y=(5/2)*x</p>
<p>Because AB slope is 5/2, BC/AC is 5/2, so its either A or B. A is right because of Pythagorean Theorem ( 2^2 + 5^2 = sqrt29)</p>
<p>The answer is A.</p>
<p>2) The total square 1x1 of the there card is 9. So among I,II,III, only II comprises of 9 1x1 squares (I and III has 8 squares only). Then try to arrange three cards in II, it’s true. so the answer is C.</p>
<p>1) Triangles with congruent angles are similar ( correct me if i’m wrong)
You can treat that this figure has 2 triangles. ABC and the large triangle (connect the points from (0,0), (4, 10) and (0,10)–> we’ll call this triangle DEF. Triangles DEF and ABC are all similar because we the hypothenuses of the two triangles lie on the same angle and it tells us it’s parallel to both teh x and y-axis. Therefore this means while ABC is smaller than DEF, we can tell that the angles and the corresponding angles are all congruent. Similar triangles always have side lengths in ratio. </p>
<p>DEF= 4 (the length of the x-axis from the origin to (4,10), 10 (from origin to y-axis of 4,10) and the hypothenuse is radical 116. </p>
<p>ABC must be in a ratio. we can tell that A is half of 4(2) and 10(5). While (radical 112)/2 is not a choice you simply do it in your calculator and see that radical 29 is the same.</p>
