Difference between revisions of "2007 AMC 8 Problems/Problem 14"
(Created page with '== Problem == The base of isosceles <math>\triangle ABC</math> is <math>24</math> and its area is <math>60</math>. What is the length of one of the congruent sides? <math>\math…') |
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== Solution == | == Solution == | ||
− | The area of a triangle is shown by <math>\frac{1}{2}bh</math>. | + | The area of a triangle is shown by <math>\frac{1}{2}bh</math>. We set the base equal to <math>24</math>, and the area equal to <math>60</math>, and we get the height, or altitude, of the triangle to be <math>5</math>. In this isosceles triangle, the height bisects the base, so by using the Pythagorean Theorem, <math>a^2+b^2=c^2</math>, we can solve for one of the legs of the triangle (it will be the the hypotenuse, <math>c</math>). |
+ | <math>a = 12</math>, <math>b = 5</math>, | ||
+ | <math>c = 13</math>. | ||
+ | The answer is <math>\boxed{\textbf{(C)}\ 13}</math> | ||
− | + | ==Video Solution by WhyMath== | |
+ | https://youtu.be/9sVdsKcpJ9U | ||
− | + | ~savannahsolver | |
− | + | ==Video Solution by SpreadTheMathLove== | |
+ | https://www.youtube.com/watch?v=omFpSGMWhFc | ||
− | + | ==Video Solution by AliceWang== | |
+ | https://youtu.be/U8v4XVPXr18 | ||
− | + | ==See Also== | |
− | + | {{AMC8 box|year=2007|num-b=13|num-a=15}} | |
− | + | {{MAA Notice}} | |
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Latest revision as of 14:32, 8 July 2024
Contents
Problem
The base of isosceles is and its area is . What is the length of one of the congruent sides?
Solution
The area of a triangle is shown by . We set the base equal to , and the area equal to , and we get the height, or altitude, of the triangle to be . In this isosceles triangle, the height bisects the base, so by using the Pythagorean Theorem, , we can solve for one of the legs of the triangle (it will be the the hypotenuse, ). , , . The answer is
Video Solution by WhyMath
~savannahsolver
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=omFpSGMWhFc
Video Solution by AliceWang
See Also
2007 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.