Question

The perimeter of a rectangle and a square are 160 m each. The area of the
rectangle is less than that of the square by 100 sq, metres. The length of the
rectangle is​

Answer 1

Solution :-

Given : The perimeter of a rectangle and a square are 160 m each.

Side of square = Perimeter / 4 = 160/4 = 40 m

Area of square = (side)² sq. units

= (40 × 40) m²

= 1600 m²

Given that, Area of the rectangle is less than that of the square by 100 sq metres.

So, Area of rectangle = Area of square - 100 m²

= (1600 - 100) m²

= 1500 m²

Now,

Perimeter of rectangle = 2(l + b) = 160 m

=> l + b = 80

=> b = 80 - l ______(i)

Area of rectangle = l × b = 1500 m²

=> l (80 - l) = 1500 [from equation (i)]

=> 80l - l² = 1500

=> l² - 80l + 1500 = 0

=> l² - 30l - 50l + 1500 = 0

=> l(l - 30) - 50(l - 30) = 0

=> (l - 30) (l - 50) = 0

=> l = 30 or l = 50

Putting the value of l in equation (i) we get,

=> b = 80 - 30 or b = 80 - 50

=> b = 50 or b = 30

Hence,

Length of the rectangle = 50 m

[ usually length is greater than breadth]

Answer 2

SOLUTION

Side of square:

$= > \frac{160}{4} = 40m$

Area of square:

$= > 40 \times 40 = 1600m {}^{2}$

Let x= length of rectangle

let y=width of rectangle

=)2x+2y= 160

=) x+y= 80

=) y= 80-x

Now,

Area of rectangle= x× y= x(80-x)

$= > 80x - {x}^{2}$

Area of square- area of rectangle=100

=) 1600-(80x-x^2)= 100

=) 1600-80x+x^2 = 100

=) x^2-80x+1500=0

=) x^2 -30x-50x +1500=0

=) x(x-30) -50(x-30)=0

=) (x-30) (x-50)=0

=) x= 30 or x= 50

The length of rectangle is 50m

hope it helps ☺️