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Question
City B is 5 miles east of city A. City C is 10 miles southeast of city B. Which of the following is the closest to the distance from city A to City C?
11 miles
12 miles
13 miles
14 miles
ANSWER : 4
Descrption
Here , AB = 5 miles, BC = 10 miles <math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>B</mi><mi>D</mi><mi>C</mi><mo> </mo><mi>i</mi><mi>s</mi><mo> </mo><mi>a</mi><mi>n</mi><mo> </mo><mi>i</mi><mi>s</mi><mi>o</mi><mi>s</mi><mi>c</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>s</mi><mo> </mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo> </mo><mo> - </mo><mi>a</mi><mi>n</mi><mi>g</mi><mi>l</mi><mi>e</mi><mi>d</mi><mo> </mo><mi>t</mi><mi>r</mi><mi>i</mi><mi>a</mi><mi>n</mi><mi>g</mi><mi>l</mi><mi>e</mi><mo>.</mo><mspace linebreak = "newline"/><mo>.</mo><mo>'</mo><mo>.</mo><mo> </mo><mi>B</mi><msup><mi>C</mi><mn>2</mn></msup><mo> = </mo><mi>B</mi><msup><mi>D</mi><mn>2</mn></msup><mo> + </mo><mi>C</mi><msup><mi>D</mi><mn>2</mn></msup><mspace linebreak = "newline"/><mo>⇒</mo><msup><mn>10</mn><mn>2</mn></msup><mo> = </mo><msup><mi>x</mi><mn>2</mn></msup><mo> + </mo><msup><mi>x</mi><mn>2</mn></msup><mspace linebreak = "newline"/><mo>⇒</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo> = </mo><mn>100</mn><mspace linebreak = "newline"/><mo>⇒</mo><msup><mi>x</mi><mn>2</mn></msup><mo> = </mo><mn>50</mn><mo> = </mo><mn>25</mn><mo>×</mo><mn>2</mn><mspace linebreak = "newline"/><mo>⇒</mo><mi>x</mi><mo> = </mo><mn>5</mn><msqrt><mn>2</mn></msqrt><mspace linebreak = "newline"/><mo>.</mo><mo>'</mo><mo>.</mo><mo> </mo><mi>A</mi><mi>D</mi><mo> = </mo><mi>A</mi><mi>B</mi><mo> + </mo><mi>B</mi><mi>D</mi><mo> </mo><mo> = </mo><mn>5</mn><mo> </mo><mo> + </mo><mn>5</mn><msqrt><mn>2</mn></msqrt><mspace linebreak = "newline"/><mi>N</mi><mi>o</mi><mi>w</mi><mo>,</mo><mo> </mo><mi>A</mi><msup><mi>C</mi><mn>2</mn></msup><mo> = </mo><mo>(</mo><mn>5</mn><mo> + </mo><mn>5</mn><msqrt><mn>2</mn></msqrt><msup><mo>)</mo><mn>2</mn></msup><mo> </mo><mo> + </mo><mo>(</mo><mn>5</mn><msqrt><mn>2</mn></msqrt><msup><mo>)</mo><mn>2</mn></msup><mspace linebreak = "newline"/><mo> = </mo><mo>(</mo><mn>5</mn><mo> + </mo><mn>5</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>414</mn><msup><mo>)</mo><mn>2</mn></msup><mo> </mo><mo> + </mo><mn>50</mn><mo> = </mo><mn>195</mn><mo>.</mo><mn>68</mn><mspace linebreak = "newline"/><mo>⇒</mo><mi>A</mi><mi>C</mi><mo> = </mo><mn>13</mn><mo>.</mo><mn>99</mn><mo> </mo><mo>≃</mo><mo> </mo><mn>14</mn></math>
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