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If a square and a rectangle have the same perimeter why does the square have a larger area?
Wiki User
∙ 15y ago
The area is given by xy and the perimter is given by 2x + 2y, where x is the side length and y is the height. So we have two equations: A = xy, P = 2x + 2y. Because the square and the rectangle have the same perimeter, P will be a constant, say 40. We can simplify this to the equivalent 20 = x + y by dividing both sides by 2. We can then rearrange it to y = 20 - x or vice versa for x and y. By substituting this into the first equation, we get A = x(20 - x) = 20x - x2. By using differentiation, we can find the x value for which A is maximum: A' = 20 - 2x Set A' to 0 (we know this will be a maximum because the x2 coefficient is negative): 0 = 20 - 2x 2x = 20 x = 10. Now we back-substitute this value for x into the equation for y: y = 20 - x = 20 - 10 = 10. Thus, the maximum area occurs when x = 10 and y = 10 i.e. when the shape is a square. This works for any starting value of the perimeter, and means that a square will always have more area than any rectangle with an equal perimeter.
Wiki User
∙ 15y ago
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The larger the perimeter of a square the larger the area of that square?
The area of a square is a function of the perimeter of the square.
What are the dimensions of the rectangle with this perimeter and an area of 8000 squares meters?
what are the dimensions of the rectangle with this perimeter and an area of 8000 square meters
Do figures with the same perimeter have the same area?
not necessarily. take the example of a 3x3 square and a 4x2 rectangle. Both have a perimeter of 12. but the square has an area of 9 and the rectangle has an area of 8.
What is the perimeter of a rectangle if the area is 360 square centimeters?
Anything from almost 75,9 (if the rectangle were a square with each side 18,97 cm) to much larger, 722 if the rectangle is 1 cm by 360 cm or if the rectangle were 0,5 by 720 cm - still an area of 360 cm2! - the perimeter would be 1441cmGreater than 4 * sqrt 360
What is the maximum area for a rectangle whose perimeter is 136?
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.
The area of a rectangle is 100 inches the perimeter is 40 a second rectangle has the same area but a different perimeter. Is the second rectangle a square?
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.
Is the perimiter of 11 by 12 rectangle smaller or larger than the perimiter of a sqare with the same area?
11 x 12 rectangle has a larger perimeter = 46 units The 132 square unit area will give a square a perimeter of 45.9565 units
Is it sometimes always or never true that the perimeter of a rectangle is numerically greater than its area?
Sometimes. Experiment with a small square and with a large square (though any shape rectangle will do). A square of 4 x 4 has a perimeter of 16, and an area of 16. A smaller square has more perimeter than area. A larger square has more area than perimeter.
The larger the perimeter of a square the larger the area of that square?
The area of a square is a function of the perimeter of the square.
The area of a rectangle is 100 square inches The perimeter of the rectangle is 40 inches A second rectangle has the same area but a different perimeter Is the second rectangle a square?
yes
If you have an area of 100 square meters what is the perimeter?
40 meters.
What is the perimeter of a 10cm square?
What is a rectangle were the area is 10 and the perimeter
What are the dimensions of the rectangle with this perimeter and an area of 8000 squares meters?
what are the dimensions of the rectangle with this perimeter and an area of 8000 square meters
Area and perimeter of plane figures?
the area and perimeter of the plane figures are square ,rectangle
What is the perimeter of a rectangle if the area is 144 square centimeters?
If the rectangle is a square, the perimeter is 48 cm. If not, there are a lot of possibilities.
What is the perimeter of a rectange if the areas 405 yd?
The perimeter of a rectangle cannot be calculated by just knowing the area unless the rectangle is a square. In which case the perimeter will be 4 x square root of the area.
What is the difference between perimeter and area of polygon?
perimeter is the measure around the figure; area is the measure within the figure formula: perimeter: length+length+width+width=perimeter (for square or rectangle) area: length times width= area ( for square or rectangle)
