Question

a rectangle and a square have the same perimeter of 100 m. find the side of the square. if the rectangle has a breadth 2m less than that of the square find the length and area of the rectangle.

Answer 1

perimeter of square =4a=100
a=100/4=25

then the breath of rectangle is =25-2=23
so the length is =25+2=27(for keeping the perimeter constant)
then the area of the rectangle is=27×23=621sq. m.

Answer 2

Solutions :-

Given :
Perimeter of rectangle = Perimeter of Square = 100 m


Find the side of the square :-

Perimeter of Square = 4 × side
=> 100 m = 4 × Side
=> Side = 100/4 = 25 m


Breadth of rectangle = (side of square - 2) m
= (25 - 2) m = 23 m

Let the length of rectangle be x

Find the length of rectangle :-

Perimeter of rectangle = 2(Length +Breadth)
=> 100 = 2(x + 23)
=> 100/2 = x + 23
=> 50 - 23 = x = 27 m


Find the area of rectangle :-

Area of rectangle = (Length × Breadth) sq. units
= (27 × 23) m²
= 621 m²


Hence,
Length of Rectangle = 27 m
Area of rectangle = 621 m²

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