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What is the greatest possible area for a rhombus constructed on a 3 by 9 sheet of paper?

 Dec 19, 2019

Best Answer 

 #1
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A rhombus is a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides.  A rhombus inscribed in a rectangle touches the sides of the rectangle so by this we can infer that the diagonals of the largest inscribed rhombus are equal to the length and breadth of the rectangle. If we have the length(l) and breadth(b) of the rectangle, the length of the diagonal of the largest rhombus inscribed inside it is d1 = l and d2 = b. The area of a rhombus is given by the formula,

Area = (d1*d2)/2

Putting in the values of d1 = 9 and d2 = 3, we get:

Area = (9*3)\2 = 27/2 = 13.5

 Dec 19, 2019
 #1
avatar+119 
+3
Best Answer

A rhombus is a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides.  A rhombus inscribed in a rectangle touches the sides of the rectangle so by this we can infer that the diagonals of the largest inscribed rhombus are equal to the length and breadth of the rectangle. If we have the length(l) and breadth(b) of the rectangle, the length of the diagonal of the largest rhombus inscribed inside it is d1 = l and d2 = b. The area of a rhombus is given by the formula,

Area = (d1*d2)/2

Putting in the values of d1 = 9 and d2 = 3, we get:

Area = (9*3)\2 = 27/2 = 13.5

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