Difference between revisions of "1987 AHSME Problems/Problem 8"
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\textbf{(D)}\ \text{between 16 and 17}\qquad | \textbf{(D)}\ \text{between 16 and 17}\qquad | ||
\textbf{(E)}\ 17</math> | \textbf{(E)}\ 17</math> | ||
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+ | == Solution == | ||
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+ | Using Pythagoras' Theorem, <math>BD = \sqrt{3^2 + 4^2} = 5</math>, and <math>AD = \sqrt{(13 - 3)^2 + 4^2} = \sqrt{116}</math>. Thus the sum is <math>5 + \sqrt{116}</math>, and as <math>100 < 116 < 121</math>, <math>10 < \sqrt{116} < 11</math>, so that the sum is between <math>5+10</math> and <math>5+11</math>, or <math>15</math> and <math>16</math>, which is answer <math>\boxed{\text{C}}</math>. | ||
== See also == | == See also == |
Latest revision as of 13:02, 1 March 2018
Problem
In the figure the sum of the distances and is
Solution
Using Pythagoras' Theorem, , and . Thus the sum is , and as , , so that the sum is between and , or and , which is answer .
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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