Answer :
Answer:
1)[tex]x^2+x-12=0[/tex]
2)[tex]x^2+8x-20=0[/tex]
3)[tex]x^2+0.9x-0.36=0[/tex]
4)[tex]2x^2-6x-36=0[/tex]
5)[tex]x^2-5x-84=0[/tex]
Step-by-step explanation:
1) The length of a wooden frame is 1 foot longer than its width and its area is equal to 12 sq. ft.
Let the width be x
We are given that length of a wooden frame is 1 foot longer than its width
So, Length = x+1
Area of rectangular frame =[tex]Length \times Breadth = x(x+1)[/tex]
ATQ
x(x+1)=12
[tex]x^2+x-12=0[/tex]
2)The length of the floor is 8 m longer than its width and there is 20 square meters.
Let the width be x
We are given that length of the floor is 8 m longer than its width
So, Length = x+8
Area of floor= [tex]Length \times Breadth = x(x+8)[/tex]
ATQ
x(x+8)=20
[tex]x^2+8x-20=0[/tex]
3)The length of a plywood is 0.9 m more than its width and its area is 0.36 m2.
Let the width be x
We are given that length of a plywood is 0.9 m more than its width
So, Length = x+0.9
Area of plywood=[tex]Length \times Breadth = x(x+0.9)[/tex]
ATQ
x(x+0.9)=0.36
[tex]x^2+0.9x-0.36=0[/tex]
4)The area of rectangle whose length is six less than twice its width is thirty-six
Let the width be x
We are given that length is six less than twice its width
So, Length = 2x-6
Area of rectangle = Length \times Breadth = x(2x-6)
ATQ
x(2x-6)=36
[tex]2x^2-6x-36=0[/tex]
5)The width of a rectangular plot is 5 m less than its length and its area is 84 m2.
Let the length be x
Width = x-5
Area =[tex]Length \times Breadth = x(x-5)[/tex]
ATQ
x(x-5)=84
[tex]x^2-5x-84=0[/tex]