Difference between revisions of "2007 AMC 8 Problems/Problem 14"
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<math>c = 13</math>. | <math>c = 13</math>. | ||
The answer is <math>\boxed{\textbf{(C)}\ 13}</math> | The answer is <math>\boxed{\textbf{(C)}\ 13}</math> | ||
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+ | ==Video Solution by WhyMath== | ||
+ | https://youtu.be/9sVdsKcpJ9U | ||
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+ | ~savannahsolver | ||
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+ | ==Video Solution by SpreadTheMathLove== | ||
+ | https://www.youtube.com/watch?v=omFpSGMWhFc | ||
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+ | ==Video Solution by AliceWang== | ||
+ | https://youtu.be/U8v4XVPXr18 | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2007|num-b=13|num-a=15}} | {{AMC8 box|year=2007|num-b=13|num-a=15}} | ||
{{MAA Notice}} | {{MAA Notice}} |
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.