This is solved by simultaneous equations. Perimeter = 2a + 2b = 100 where a and b are lengths of sides Area = a x b Rearranging the perimeter equation: 2a = 100 - 2b, a = 50 - b Putting this equation into the area equation: Area = (50 - b) x b = 50b - b x b Find the minimum/maximum by differentiating and setting to 0. Area' = 50 - 2b = 0, 2b = 50, b = 25 Area = 625cm sqare. when the length tends to 50, the area tends to 0. So the area can be anything from 0 to 625 cm
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the area of a rectangleis 100 square inches. The perimeter of the rectangle is 40 inches. A second rectangle has the same area but a different perimeter. Is the secind rectangle a square? Explain why or why not.
The perimeter of a rectangle cannot be determined with the area alone as the lengths could vary. For example, the perimeter of the rectangle could be 12 (1 and 5) or 9 (2 and 2.5). For both cases, the area is still 5cm2, but the length can still change to result in different results.
Would be congruent.It doesn't have to be a rectangle, though.It could be any shape.
No. For example, a 4x1 rectangle will have an area of 4 and a perimeter of 10. A 2x2 rectangle will have the same area of 4, but a perimeter of 8.