4t ESO/4.06 TRIGONOMETRIA/4.06.2 Semblança/4.06.2.3 Problemes de semblança 4.06.2.3.51Q Problema superfície semblant Per pintar les parets d'una habitació rectangular de #l m de llarg, #a m d'ample i #h m d'alt, s'han utilitzat #k kilos de pintura.

Quants kilos de pintura calen per pintar les parets d'una habitació semblant si fa #l2 m de llarg?

Format: arrodonit als centèsims

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>l</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mfenced><mrow><mn>201</mn><mo>,</mo><mn>650</mn></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mfenced><mrow><mn>201</mn><mo>,</mo><mn>450</mn></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mfenced><mrow><mn>201</mn><mo>,</mo><mn>260</mn></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>l</mi><mo>&gt;</mo><mi>a</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>nr</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>dr</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mfrac><mi>nr</mi><mi>dr</mi></mfrac></mtd></mtr></mtable><mrow><mi>r</mi><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>l</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>l</mi><mo>*</mo><mi>h</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S2</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>l</mi><mo>*</mo><mi>h</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>h</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mfrac><mi>S1</mi><mi>k1</mi></mfrac></mfenced><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mi>k</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.98</mn><mo>,</mo><mn>2.66</mn><mo>,</mo><mn>2.34</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>6</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>,</mo><mi>S2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35.755</mn><mo>,</mo><mn>48.667</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16.33</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">6</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es calcula la raó de semblança:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»l«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»l«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Com que la raó entre les longituds és r, la raó entre les superfícies pintades és r2.

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