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# Largest Area of Triangle | AIME I, 1992 | Question 13

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Largest Area of Triangle.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Largest Area of Triangle.

## Area of Triangle – AIME I, 1992

Triangle ABC has AB=9 and BC:AC=40:41, find the largest area that this triangle can have.

• is 107
• is 820
• is 840
• cannot be determined from the given information

Ratio

Area

Triangle

## Check the Answer

AIME I, 1992, Question 13

Coordinate Geometry by Loney

## Try with Hints

Let the three sides be 9, 40x, 41x

area = $\frac{1}{4}\sqrt{(81^2-81x^2)(81x^2-1)} \leq \frac{1}{4}\frac{81^2-1}{2}$

or, $\frac{1}{4}\frac{81^2-1}{2}=\frac{1}{8}(81-1)(81+1)$

=(10)(82)

=820.