Question

The area of a rectangle is 75m2 and width is 10m less than the length. Find the length and width of rectangle; also find the perimeter of rectangle​

Answer 1

It is given that the area of a rectangle is 75 m² and breadth of the triangle is 10 m less than the length.

Let the required length of the rectangle be a m and breadth of the rectangle be ( a - 10 ) m .

Length of the rectangle = a m

Breadth of the rectangle = ( a - 10 ) m

Area of the rectangle = 75 m^2

From the properties of quadrilateral we know that the area of rectangle is the product of its length and breadth.

= > Area of this rectangle = 75 m^2

= > a ( a - 10 ) m^2 = 75 m^2

= > a^2 - 10a = 75

= > a^2 - 10a - 75 = 0

Splitting 10 into two numbers such that the product of the parts will be equal to the product of coefficient of a^2 and 75.

Product of coefficient of a^2 and 75 = 1 x 75 = 75.

And, therefore the required parts should be 15 and 5, as 15 - 5 is equal to 10,also the product of 15 and 5 is 75.

= > a^2 - ( 15 - 5 )a - 75 = 0

= > a^2 - 15a + 5a - 75 = 0

= > a( a - 15 ) + 5( a - 15 ) = 0

= > ( a + 5 )( a - 15 ) = 0

By Zero Product Rule, a = - 5 or 15.

Since a is assumed as side of rectangle , it can't be negative.

Hence the value of a is 15.

It means, length of the rectangle = a m = 15 m and breadth of the rectangle = ( a - 10 ) m = ( 15 - 10 ) m = 5 m.

We know :

Perimeter of rectangle = 2( length + breadth)

= > Perimeter of this rectangle = 2( 15 + 5 ) m

= > Perimeter of this rectangle = 2 x 20 m

= > Perimeter of this rectangle = 40 m

Hence,

Perimeter of the rectangle is 40 m.

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Answer 2

Let the length be X.

so, width is x-10m.

A/Q

x-10=75 m2

X = 75+10 = 85

Now,

Length= X=85 and,

width = x-10 = 85-10 = 75.

>The Perimeter of rectangle =2×( Length+Breadth)

=2×( 85+75)

=2×150

=300 Ans.

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