The diagonal of the rectangle is 18, what is the largest area this rectangle can have
| April 16, 2021 | education
A rectangle is a convex rectangle whose area is: S = d1 * d2 * Sinα, where d1, d2 are the diagonals of the quadrilateral, and sinα is the angle between them.
Since AВСD is a rectangle, its diagonals are equal, AC = ВD = 18 cm.
Savsd = 162 * SinAOB.
The maximum area of the rectangle will be at SinAOB = 1.
Then the angle AOB = 90, and the quadrangle AOСD is a square.
Answer: The maximum area is 162 cm2.
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