Question

the length of the rectangular playground is 2m larger than its breath if the area of playground is 195m square find the length and breath of field.
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Answer 1

Answer :

13 m

Given :

Area of the rectangular playground = 195 m²

To find:

Length = ?

Breadth = ?

Solution:

Let the breadth of the rectangular playground = b  

Length of the rectangular playground = (b + 2)

Area of rectangular playground = Length × Breadth

= 195 = (b + 2) × b

= 195 = b² + 2b

=  b²+2b − 195  =  0

= b²+ 15b - 13b − 195  =  0

= b (b + 15) − 13 (b + 15)  =  0

= ( b − 13)  (b  +  15)  =  0

= b  =  13 or  b  =  −15

The value cannot be minus

Therefore, breadth of the rectangular playground  =  13  m  

and length of the rectangular playground  =  15  m

Answer 2

Topic

Quadratic Equation

Given

The length of the rectangular playground is 2m larger than its breadth.

Area of playground is 195m².

To Find

Length and Breadth of Playground

Solution

Method

Form an equation with given data and solve it for length and breadth.

Let breadth of playground be x.

Then length will be ( x + 2 ).

Note :-

Area of rectangle = Length * Breadth

195 = ( x + 2 )( x )

x² + 2x -195 = 0

x² + 15x - 13x - 195 = 0

x( x + 15 ) - 13( x + 15 ) = 0

( x + 15 )( x - 13 ) = 0

Now, we will take cases,

x + 15 = 0

x = -15

We will reject this value as breadth can't be negative.

x - 13 = 0

x = 13

So, breadth of playground is 13 m. And

length is ( x + 2 ) = ( 13 + 2 ) = 15 metres.

Answer

So, length of rectangular playground is 15 metres and breadth is 13 metres.

Learn More :-

Rectangle

It is a parallelogram.

Opposite sides are equal.

Diagonal are equal.

All interior angles are right angle.