Difference between revisions of "2017 AIME I Problems/Problem 4"
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| − | Let the triangular base be <math>\triangle ABC</math>. | + | ==Problem 4== |
| + | A pyramid has a triangular base with side lengths <math>20</math>, <math>20</math>, and <math>24</math>. The three edges of the pyramid from the three corners of the base to the fourth vertex of the pyramid all have length <math>25</math>. The volume of the pyramid is <math>m\sqrt{n}</math>, where <math>m</math> and <math>n</math> are positive integers, and <math>n</math> is not divisible by the square of any prime. Find <math>m+n</math>. | ||
| + | ==Solution== | ||
| + | Let the triangular base be <math>\triangle ABC</math>. Using Simplified Heron's formula for the area of an isosceles triangle gives <math>12\sqrt{32(8)}=192</math>. | ||
Revision as of 16:09, 8 March 2017
Problem 4
A pyramid has a triangular base with side lengths 
, , and 
. The three edges of the pyramid from the three corners of the base to the fourth vertex of the pyramid all have length 
. The volume of the pyramid is 
, where 
and 
are positive integers, and is not divisible by the square of any prime. Find 
.
Solution
Let the triangular base be 
. Using Simplified Heron's formula for the area of an isosceles triangle gives 
.
