M7MBA wrote:Triangle ABC has a perimeter of 18. Which of the following cannot be the area of triangle ABC?
(A) 119/359
(B) 359/119
(C) π
(D) 12
(E) 16
Given a FIXED PERIMETER for a triangle, the greatest possible are will be yielded if the triangle is EQUILATERAL.
The area of an equilateral triangle = (s²/4)√3.
√3 ≈ 1.7.
If a triangle with a fixed perimeter of 12 is equilateral -- implying that each side has a length of 4 -- we get:
Greatest possible area = (s²/4)√3 = (4²/4)√3 = 9√3 ≈ (9()(1.7) = 15.3.
Thus, the area cannot be equal to 16.
The correct answer is
E.
A similar rule:
Given a quadrilateral with a fixed perimeter, the greatest possible area will be yielded if the quadrilateral is a SQUARE.
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