Question

The perimeter of a rectangular piece land is 130m and its area is 1000sq.m find it's dimensions.
please give step by step explanation​

Answer 1

Length = l m

Breadth = b m

Perimeter = 130 m

2 ( l + b ) = 130

l + b = 65 -----( 1 )

Area = 1000 m²

lb = 1000 ---( 2 )

( l - b )² = ( l + b )² - 4lb

= ( 65 )² - 4 × 1000

= 4225 - 4000

= 225

l - b = √ 225

l - b = 15 -----( 2 )

Add ( 1 ) and ( 2 ) equations , we get

2l = 80

l = 40 m

Put l = 40 in equation ( 2 ) , we get

40 × b = 1000

b = 1000/40

b = 25 m

Therefore ,

l = 40 m

b = 25 m

I hope this helps

Answer 2

Step-by-step explanation:

perimeter of a rectangle is 2(l+b) .

2(l+b) = 130_____(1)

l+b =130/2

l+b =65

l = 65 -b______(2)

Area of rectangle is l×b.

l×b =1000_____(3)

Substitute l=65-b in equation (3)..

(65-b)×b =1000

65b -b^2 =1000

b^2-65b +1000 = 0

b^2- 40b - 25b +1000 =0

(b-40)(b-25) =0

b=40 or 25

substitute b=25 in equation (2)

l = 65 - 25

l = 40

Length =40cm and breadth = 25cm.