The perimeters of a square and a rectangle are equal If their areas be A m2 and B m2 , - Maths - Perimeter and Area

Question

The perimeters of a square and a rectangle are equal If their
areas be A m2 and B m2 , then which of the following is a true
statement
AA is less than equal to BA BA is greater than equal to B

Ajanta Trivedi · Accepted Answer

let the equal perimeter be p m let the length of the side of square be x m and the length and breadth of rectangle be l m and b m therefore $4 x = p \Rightarrow x = \frac{p}{4}$ area of the square : $A = x^{2} = (\frac{p}{4})^{2} = \frac{p^{2}}{16} m^{2}$ perimeter of the rectangle is $2 (l + b) = p l + b = \frac{p}{2}$ area of the rectangle $B = l b$ since $\frac{l + b}{2} \geq \sqrt{l b}$ thus $B = l b \leq (\frac{l + b}{2})^{2} B \leq (\frac{p}{4})^{2} B \leq \frac{p^{2}}{16} B \leq A$ thus the area of the rectangle is less than or equal to area of the square hope this helps you cheers!!

The perimeters of a square and a rectangle are equal.If their areas be A m2 and B m2 , then which of the following is a true statement.AA is less than equal to BA BA is greater than equal to B

The perimeters of a square and a rectangle are equal.If their areas be A m2 and B m2 , then which of the following is a true statement.
AA is less than equal to BA BA is greater than equal to B