Question

the area of a rectangular field is 120 sq.m and its perimeter is 46 m , what are its dimensions?

Answer 1

Let the length be x and breadth be y,
we know that,
area of rectangle=lb
120=xy
120/x=y........(¡)
Perimeter of rectangle=2 (l+b)
46=2 (x+y)
23=x+y ......(¡¡)

from ¡ and ¡¡,
23=x+120/x
23=x^2+120/x
x^2-23x+120=0
by middle splitting,
x^2-15x-8x+120=0
x (x-15)-8 (x-15)=0
(x-8)(x-15)=0

hence,x=8 or 15

so,length=8 m
breadth=y=120/8=15 m.


I have given my 100%effort to solve it...thank u

Answer 2

Its dimensions are 15 cm and 8 cm

Step-by-step explanation:

Let the length be x and breadth be y

Area of rectangle =$Length \times Breadth = xy$

We are given that the area of a rectangular field is 120 sq.m

So, xy = 120

$x=\frac{120}{y}$

Perimeter of rectangular field =2(l+b)=2(x+y)

We are given that its perimeter is 46 m

2(x+y)=46

x+y=23

$\frac{120}{y}+y=23\\120+y^2=23y\\y^2-23y+120=0$

(y-15)(y-8)=0

So, y = 15, 8

Hence Its dimensions are 15 cm and 8 cm

#Learn more:

The area of a rectangular carpet is 120 m square and its perimeter is 46 M the length of its diagonal is

https://brainly.in/question/2641954