Triangle
The sides of a triangle are and . What is the largest possible area of the triangle, if
Write your answer to 3 decimal places.
The answer is 1.000.
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1 solution
To make the area as large as possible, the sides should be large.
But going for the maximum, 1,2, and 3, will result in a degenerate triangle with area zero.
Keeping the two smaller numbers as large as possible, what shape would give the highest area?
The area would be the highest if the two were perpendicular to each other.
The longest side will then be c = 1 + 4 = 5 ≈ 2 . 2 3 6 , which is between 2 and 3 as required.
The area is 2 1 × 1 × 2 = 1
(Shrinking either of the legs clearly does not increase the area, so this is the solution.)