Question

Learning Task 2.

A. Translate the following verbal sentences to mathematical sentence. Then ex-
press into quadratic equations in terms of "x".
Given
Quadratic Equations
1. The length of a wooden frame is 1 foot
longer than its width and its area is equal
to 12 ft2
2. The length of the floor is 8 m longer than
its width and there is 20 square meters.
3. The length of a plywood is 0.9 m more
than its width and its area is 0.36 m2.
4. The area of rectangle whose length is six
less than twice its width is thirty-six,
5. The width of a rectangular plot is 5 m
less than its length and its area is 84 m2.☹️​

Answer 1

1)
`x^2+x-12=0`

2)
`x^2+8x-20=0`

3)
`x^2+0.9x-0.36=0`

4)
`2x^2-6x-36=0`

5)
`x^2-5x-84=0`

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 =
`Length * Breadth = x(x+1)`

ATQ

x(x+1)=12

`x^2+x-12=0`

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=
`Length * Breadth = x(x+8)`

ATQ

x(x+8)=20

`x^2+8x-20=0`

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=
`Length * Breadth = x(x+0.9)`

ATQ

x(x+0.9)=0.36

`x^2+0.9x-0.36=0`

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

`2x^2-6x-36=0`

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 =
`Length * Breadth = x(x-5)`

ATQ

x(x-5)=84

`x^2-5x-84=0`