Question

A rectangle and the square have the same perimeter 100 cm find the side of the square . If the rectangle has breadth 2 cm less than the side of square find the breadth , length and th area of the rectangle ​

Answer 1

Answer:

Side of square = 25 cm. Breadth of rectangle = 23 cm

Answer 2

Given :-  

• A rectangle and the square have the same perimeter 100 cm

• The rectangle has breadth 2 cm less than the side of square  

To Find :-  

• The side of the square  , measures of rectangle including it's area

Solution :-  

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As we know that ,  

• Perimeter of a Square = 4( Side )  

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Finding the side of the square -  

$\sf \implies 100\;cm = 4( Side )$

$\sf \implies Side = \dfrac{100}{4}$

$\sf \implies Side = 25\;cm$  

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ATQ ::  

Breadth = ( Side of Square ) – 2

Breadth = 23 cm  

As we know that ,  

Perimeter of rectangle = 2( l + b )  

Where ,  

• l is length  
• b is breadth  

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Finding the length –  

$\sf \implies 2( l + 23 ) = 100\;cm$  

$\sf \implies l + 23 = \dfrac{100}{2}$

 

$\sf \implies l + 23 = 50\;cm$ 

$\sf \implies l = 50 - 23$

$\sf \implies l = 27\;cm$

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As we  know that ,  

Area of rectangle = lb  

Where ,  

• l is length  
• b is breadth  

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Finding the area –  

$\sf \implies 23\;cm \times 27\;cm$

$\sf \implies 621\;cm^{2}$

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Therefore ,  

• Length and breadth of rectangle are 23 cm and 27 cm  
• Area of rectangle is 621 cm
• Side of the square is 25 cm  

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