Question

The area of a rectangle field is 120 sqm and it's perimeter is 46m what are it's dimensions

Answer 1

Area=l×b
120m²=l×b
120/l=b-----------eq.1


P=2(l+b)
46=2(l+b)
23=l+b-------------eq.2

Putting b in 23=l+b(eq.2)
23=l+120/l
23=l²+120/l
23l=l²+120
l²-23l+120=0
l²-15l-8l+120=0
l(l-15)-8(l-15)=0
(l-15)(l-8)=0

l=15
l=8

Since length is always greater we will take length(l)=15

Putting l in eq.2=23=l+b
23=15+b
23-15=b
8=b


Length =15m
Breath=8m

Answer 2

Let the length be l m and breadth be b m.

Given, Area of rectangle field = 120 m^2.

Area of rectangle = length × breadth

120 = l × b

120 / b = l

Perimeter of rectangle field = 46 m.

Perimeter of rectangle = 2 ( length + breadth)

46 =2 × ( l + b )

46 / 2 = l + b

23 = l + b

Putting value of l,

23 = 120 / b + b

b^2 + 120 = 23 b

b ^2 - 23 b + 120 = 0.

b^2 - 15 b - 8 b + 120 = 0

b ( b - 15 ) - 8( b - 15 ) = 0

( b - 15 ) ( b - 8 ) = 0

( b - 15 ) = 0

( b - 8 ) = 0

b = 15, 8.

Putting value of b ( 15 m ) in l,

L = 120 / b = 120 / 15 = 8 m.

So, Length = 8 m, breadth = 15 m.

OR

Putting value of b ( 8 m ) in l,

L = 120 / b = 120 / 15 = 8 m.

So, Length = 8 m, breadth = 15 m.

=> Dimensions of the field are 15 m and 8 m.