2017 AIME I Problems/Problem 4

Problem 4

A pyramid has a triangular base with side lengths $20$ , $20$ , and $24$ . The three edges of the pyramid from the three corners of the base to the fourth vertex of the pyramid all have length $25$ . The volume of the pyramid is $m\sqrt{n}$ , where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n$ .

Solution

Let the triangular base be $\triangle ABC$ . Using Simplified Heron's formula for the area of an isosceles triangle gives $12\sqrt{32(8)}=192$ .

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2017 AIME I Problems/Problem 4

Problem 4

Solution