Question

Peremeter of a rectangle is 70 cm and its area 300cm fing leng and bredth

Answer 1

Answer:

The dimensions of the rectangle are 15 and 20cm.

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Explanation:

Given that: Perimeter of a rectangle is 70 cm

Area of the rectangle is 300 cm.

Need to find: Length and Breadth

Concept:

Perimeter of a triangle = 2( l + b )

Area of rectangle = l × b

Where,

• L denotes length
• B denotes breadth

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Solution :

~By putting the values in the formula of finding perimeter.

$\sf : \implies Perimeter = 70 ; cm$

$\sf : \implies 2( l + b) = 70$

$\sf : \implies l + b = \dfrac{70}{2}$

$\sf : \implies l + b = 35$

$\sf \leadsto b = 35 - l$

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~By putting the values in the formula of finding area.

$\sf : \implies Area = 300 cm$

$\sf : \implies l × b = 300 cm$

$\sf : \implies l × ( 35 - l ) = 300$

$\sf : \implies 35l - l^{2} = 300$

$\sf : \implies 35l - l^{2} - 300 = 0$

$\sf : \implies l^{2} - 20l - 15l - 300 = 0$

$\sf : \implies l( l - 20 ) - 15( l - 20 ) = 0$

$\sf : \implies ( l - 20 )( l - 15 ) = 0$

$\sf : \implies l - 20 = 0$

$\sf : \implies l - 15 = 0$

$\sf \leadsto l = 20$

$\sf \leadsto l = 15$

$\sf : \implies b = 35 - l$

$\sf \leadsto b = 20$

$\sf \leadsto b = 15$

~As taken as general, length is bigger tha breadth. So, we will consider length as 20 cm and breadth as 15 cm.

$\boxed{\bf{ l = 20 cm}} \star$

$\boxed{\bf{ b = 10 cm}} \star$