MathDB

A trapezoid has side lengths

3, 5, 7,

and

11

. The sum of all the possible areas of the trapezoid can be written in the form of

r_1 \sqrt{n_1} + r_2 \sqrt{n_2} + r_3

, where

r_1, r_2,

and

r_3

are rational numbers and

n_1

and

n_2

are positive integers not divisible by the square of a prime. What is the greatest integer less than or equal to

r_1 + r_2 + r_3 + n_1 + n_2?

<span class='latex-bold'>(A)</span>\ 57\qquad<span class='latex-bold'>(B)</span>\ 59\qquad<span class='latex-bold'>(C)</span>\ 61\qquad<span class='latex-bold'>(D)</span>\ 63\qquad<span class='latex-bold'>(E)</span>\ 65

Problem Statement