The maximum area for a rectangle of fixed perimeter is that of the square that can be formed with the given perimeter. 136/4 = 34, so that the side of such a square will be 34 and its area 342 = 1156.
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The perimeter of the rectangle is the sum of its 4 sides.
The length of a rectangle is twice its width. If the perimeter of the rectangle is , find its area.
find the perimeter and area of a rectangle that is 15cm long and 5cm wide
Let's take a look at this problem.Rectangle Perimeter = 2(l + w)Rectangle Perimeter =? 2(2l + 2w)Rectangle Perimeter =? (2)(2)(l + w)2(Rectangle Perimeter) = 2[2(l + w)]Thus, we can say that the perimeter of a rectangle is doubled when its dimensions are doubled.Rectangle Area = lwRectangle Area =? (2l)(2w)Rectangle Area =? 4lw4(Rectangle Area) = 4lwThus, we can say that the area of a rectangle is quadruplicated when its dimensions are doubled.
The maximum area is attained when the rectangle is, in fact, a square. Since the perimeter = 48 feet, the maximum length for a square = 48/4 = 12 feet. So max area = 122 = 144 square feet.