Which type of rectangle with given perimeter has the largest area?

Hence, the area is maximum when the rectangle is a square. Show that of all the rectangles with a given perimeter, the square has the largest area.

Why does a square have the largest area?

Because they have the same perimeter we can say A+B=2C. so the area of the square will be greater than that of the rectangle by the square of difference of the sides length.

Is the rectangle with the largest area a square?

The largest possible rectangular area is in the shape of a square.

Why do squares have the smallest perimeter?

Since there is no rule that states a rectangle cannot have all sides of equal length, all squares are rectangles, but not rectangles are squares. Hence, the minimum perimeter is 16 in with equal sides of 4 in.

Do rectangles with the same perimeter have the same area?

We found that the 6 by 3 rectangle works, because 6+3+6+3=18 and 6×3=18, so this has equal area and perimeter. But if both the length and the width are odd, then the area will be odd, meaning that it is impossible for the perimeter to be the same as the area.

How do you find the minimum perimeter of a rectangle when given the area?

P = 2sqrt(A) + 2sqrt(A) = 4sqrt(A). The area of a rectangle is the length and width of the rectangle，so we suppose the area is s ， the length is x and the width is s/x，the perimeter is 2*（x+s/x），the minimum perimeter is 2√s.

What is the perimeter of a 5cm square?

perimeter of a square is four times its one side. As side of the square is 5 cm. Its perimeter is 5×4=20 cm.

How do you find the perimeter of the area is given?

To get the perimeter from the area for a square, multiply the square root of the area times 4 . Perimeter is always measured in linear units, which is derived from the area’s square units.

Which rectangles with a given perimeter have the largest area?

Show that of all the rectangles with a given perimeter, the square has the largest area. Please log in or register to add a comment. Let the length and breadth of rectangle be x and y. Therefore, for largest area of rectangle x=y=P/4 i.e., with given perimeter, rectangle having largest area must be square.

How do you find the area of a rectangle with X?

Let P be the fixed perimeter of a rectangle with length x and height y, so that P = 2x + 2y. The area is A = xy. We can write this as a function of x by solving P = 2x + 2y for y and substituting: P = 2x + 2y ⇒ 2y = P − 2x ⇒ y = P 2 − x ⇒ A = f (x) = x( P 2 − x) = ( P 2)x − x2 (for 0 < x < P 2 ).

Which rectangle has the greatest area P4 or P2?

When x = P 4, then y = P 2 − P 4 = P 4 as well. This implies that the dimensions of the rectangle are all equal and it’s actually a square. In other words, for all rectangles of a given perimeter P, the square of side length P 4 has the greatest area.

How do you find the length and breadth of a rectangle?

Let x, y be the length and breadth of rectangle whose area is A and perimeter is P. Hence, for smallest perimeter, length and breadth of rectangle are equal (x = y = √A) i. e. , rectangle is square.