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Question
what is the area of the triangle BCD?
40
42
44
48
ANSWER : 4
Descrption
<pre><math xmlns = "http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo> </mo><mo>∆</mo><mi>A</mi><mi>B</mi><mi>C</mi><mo>,</mo><mo> </mo><mi>A</mi><mi>B</mi><mn>2</mn><mo> = </mo><mi>A</mi><mi>C</mi><mn>2</mn><mo> + </mo><mi>B</mi><mi>C</mi><mn>2</mn><mspace linebreak = "newline"/><mo>⇒</mo><mo>(</mo><mn>10</mn><mo>)</mo><mn>2</mn><mo> = </mo><mo>(</mo><mn>6</mn><mo>)</mo><mn>2</mn><mo> + </mo><mi>B</mi><mi>C</mi><mn>2</mn><mspace linebreak = "newline"/><mo>⇒</mo><mi>B</mi><mi>C</mi><mn>2</mn><mo> = </mo><mo>(</mo><mn>10</mn><mo>)</mo><mn>2</mn><mo> - </mo><mo>(</mo><mn>6</mn><mo>)</mo><mn>2</mn><mspace linebreak = "newline"/><mi>A</mi><mi>g</mi><mi>a</mi><mi>i</mi><mi>n</mi><mo> </mo><mi>f</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo> </mo><mo>∆</mo><mi>D</mi><mi>E</mi><mi>B</mi><mo>,</mo><mo> </mo><mi>D</mi><mi>B</mi><mn>2</mn><mo> = </mo><mi>D</mi><mi>E</mi><mn>2</mn><mo> + </mo><mi>B</mi><mi>E</mi><mn>2</mn><mspace linebreak = "newline"/><mo>⇒</mo><mo>(</mo><mn>13</mn><mo>)</mo><mn>2</mn><mo> = </mo><mo>(</mo><mn>5</mn><mo>)</mo><mn>2</mn><mo> + </mo><mi>B</mi><mi>E</mi><mn>2</mn><mspace linebreak = "newline"/><mo>⇒</mo><mi>B</mi><mi>E</mi><mn>2</mn><mo> = </mo><mo>(</mo><mn>13</mn><mo>)</mo><mn>2</mn><mo> - </mo><mo>(</mo><mn>5</mn><mo>)</mo><mn>2</mn><mspace linebreak = "newline"/><mo>∴</mo><mo> </mo><mi>B</mi><mi>E</mi><mo> </mo><mo> = </mo><mo> </mo><mn>12</mn><mspace linebreak = "newline"/><mi>N</mi><mi>o</mi><mi>w</mi><mo> </mo><mi>f</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo> </mo><mo>∆</mo><mi>B</mi><mi>C</mi><mi>D</mi><mo> = </mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mo>×</mo><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo> = </mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>8</mn><mo>×</mo><mn>12</mn><mo> = </mo><mn>48</mn></math> </pre>
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