Question

14. A rectangle and a square have the same perimeter of 100 cm. Find the side of the square. If the
rectangle has a breadth 2 cm less than the side of the square, find the breadth, length and area
of the rectangle.
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Answer 1

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

Answer 2

Step-by-step explanation:

Perimeter of square 4 × Side

100 = 4 × x

100÷4 = x

x=25

perimeter of rectangle 2(l+b)

breadth =25-2=23

length = 2 ( x + 23)= 100

2x + 46 = 100

2x = 100 - 46

x = 54/2

x = 26

area of rectangle l×b

26×23

598cm^2