Question

the length of a room is 3 more than twice its breadth if the area of the room is 230 metre square find the dimensions of the room​

Answer 1

perimeter of rectangle=230

2(l+b)=230

suppose breadth =x 28

and length=3x+2 =3×28+2=86

2(3x+2+x)=230

6x+4+2x=230

8x+4=230

8x=230-4

8x=226

x=226/8

x=28

Answer 2

Solution:

let the length be x+3 m and the breadth be x m.

now,

according to the formula,

Area if a rectangle= length × breadth.

230= (x+3) × x

230= x^2+3x

hence,

x^2+3x-230= 0........required quadratic polynomial.

now,

by formula method,

a= 1,b= 3 and c= -230

b^2-4ac= (3) ^2+4×230

= 9+920

= 929

Also, √929= 30.479= 30.48

now,

1.-b+√b^2-4ac

2a

-3+√929

2

-3+30.48

2

27.48/2= 13.74

2.

-b-√b^2-4ac

2a

-3-30. 48

2

-33. 48/2= -16. 74

since,

length and breadth cannot be negative,

x= -16. 74 is discarded.

hence,

breadth = 13.74 m

length= x+3= 16.74 m

hope this helps!!! ❤✌☺