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1988 AHSME Problems/Problem 2 - Revision history
2024-03-29T06:38:20Z
Revision history for this page on the wiki
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Quantummech: /* Solution */
2015-08-31T10:21:11Z
<p><span dir="auto"><span class="autocomment">Solution</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 10:21, 31 August 2015</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Since the triangles are similar, we know that the corresponding sides of the triangle are in ratio to each other. </ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">We have <math>\frac{\overline{AB}}{\overline{XY}}=\frac{\overline{BC}}{\overline{YZ}}</math>. Plugging in values we have:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><math>\frac{3}{4}=\frac{5}{\overline{YZ}}</math>. Solving for <math>\overline{YZ}</math>, we have <math>\overline{YZ}=6\frac{2}{3}</math>. So, the answer is <math>\boxed{\text{D}}</math>.</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td></tr>
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Quantummech
https://artofproblemsolving.com/wiki/index.php?title=1988_AHSME_Problems/Problem_2&diff=65558&oldid=prev
Timneh: Created page with "==Problem== Triangles <math>ABC</math> and <math>XYZ</math> are similar, with <math>A</math> corresponding to <math>X</math> and <math>B</math> to <math>Y</math>. If <math>AB=3,..."
2014-10-23T05:43:37Z
<p>Created page with "==Problem== Triangles <math>ABC</math> and <math>XYZ</math> are similar, with <math>A</math> corresponding to <math>X</math> and <math>B</math> to <math>Y</math>. If <math>AB=3,..."</p>
<p><b>New page</b></p><div>==Problem==<br />
<br />
Triangles <math>ABC</math> and <math>XYZ</math> are similar, with <math>A</math> corresponding to <math>X</math> and <math>B</math> to <math>Y</math>. If <math>AB=3, BC=4</math>, and <math>XY=5</math>, then <math>YZ</math> is: <br />
<br />
<math>\text{(A)}\ 3\frac{3}{4} \qquad <br />
\text{(B)}\ 6 \qquad <br />
\text{(C)}\ 6\frac{1}{4} \qquad <br />
\text{(D)}\ 6\frac{2}{3} \qquad <br />
\text{(E)}\ 8</math><br />
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==Solution==<br />
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== See also ==<br />
{{AHSME box|year=1988|num-b=1|num-a=3}} <br />
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[[Category: Introductory Geometry Problems]]<br />
{{MAA Notice}}</div>
Timneh