https://artofproblemsolving.com/wiki/index.php?title=1960_AHSME_Problems/Problem_21&feed=atom&action=history
1960 AHSME Problems/Problem 21 - Revision history
2024-03-29T07:20:12Z
Revision history for this page on the wiki
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Harryanvi: /* Problem */
2024-02-01T06:00:14Z
<p><span dir="auto"><span class="autocomment">Problem</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 06:00, 1 February 2024</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</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;"><div>==Problem==</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>==Problem==</div></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;"></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="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>The diagonal of square <math>I</math> is <math>a+b</math>. The <del class="diffchange diffchange-inline">perimeter </del>of square <math>II</math> with twice the area of <math>I</math> is:</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>The diagonal of square <math>I</math> is <math>a+b</math>. The <ins class="diffchange diffchange-inline">area </ins>of square <math>II</math> with twice the area of <math>I</math> is:</div></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;"></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><math>\textbf{(A)}\ (a+b)^2\qquad</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><math>\textbf{(A)}\ (a+b)^2\qquad</div></td></tr>
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Harryanvi
https://artofproblemsolving.com/wiki/index.php?title=1960_AHSME_Problems/Problem_21&diff=94560&oldid=prev
Rockmanex3: /* See Also */
2018-05-17T23:06:30Z
<p><span dir="auto"><span class="autocomment">See Also</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 23:06, 17 May 2018</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;"><div>{{AHSME 40p box|year=1960|num-b=20|num-a=22}}</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>{{AHSME 40p box|year=1960|num-b=20|num-a=22}}</div></td></tr>
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Rockmanex3
https://artofproblemsolving.com/wiki/index.php?title=1960_AHSME_Problems/Problem_21&diff=94402&oldid=prev
Rockmanex3: Solution to Problem 21
2018-05-11T00:24:33Z
<p>Solution to Problem 21</p>
<p><b>New page</b></p><div>==Problem==<br />
<br />
The diagonal of square <math>I</math> is <math>a+b</math>. The perimeter of square <math>II</math> with twice the area of <math>I</math> is:<br />
<br />
<math>\textbf{(A)}\ (a+b)^2\qquad<br />
\textbf{(B)}\ \sqrt{2}(a+b)^2\qquad<br />
\textbf{(C)}\ 2(a+b)\qquad<br />
\textbf{(D)}\ \sqrt{8}(a+b) \qquad<br />
\textbf{(E)}\ 4(a+b) </math><br />
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==Solution==<br />
Since the diagonal of square <math>I</math> is <math>a+b</math> units long, the side length of square <math>I</math> is <math>\frac{a+b}{\sqrt{2}}</math>, so the area of square <math>I</math> is <math>\frac{(a+b)^2}{2}</math>.<br />
<br />
The area of square <math>II</math> is twice as much as the area of square <math>I</math>, so the area of square <math>II</math> is <math>(a+b)^2</math>. That means the side length of square <math>II</math> is <math>a+b</math>, so the perimeter of square <math>II</math> is <math>4(a+b)</math>, or answer choice <math>\boxed{\textbf{(E)}}</math>.<br />
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==See Also==<br />
{{AHSME 40p box|year=1960|num-b=20|num-a=22}}</div>
Rockmanex3