Question

The length of a rectangular frame is represented by the expression 2x+4 and the width of the rectangular frame is represented by the expression 2x+10. Write an equation to solve for the width of a rectangular frame that has a total area of 120 square inches

2x^2+20x-80=0
4x^2+28x+40=0
4x^2+28x-80=0
x^2+8x+20=0​

Answer 1

Option 3 -
`4x^2+28x-80=0`

Explanation:

We have given,

The length of a rectangular frame is represented by the expression L=2x+4.

The width of the rectangular frame is represented by the expression B=2x+10.

The total area of a rectangular frame is A=120 square inches.

To find : Write an equation to solve for the width of a rectangular frame ?

Solution :

The area of the rectangle is given by,

`\text{Area}=\text{Length}* \text{Breadth}`

Substitute the values,

`120=(2x+4)*(2x+10)`

`120=4x^2+20x+8x+40`

`4x^2+28x+40-120=0`

`4x^2+28x-80=0`

The required equation is
`4x^2+28x-80=0`

Therefore, option 3 is correct.

Answer 2

4x^2 + 28x - 80=0

Explanation:

(2x+4)(2x+10) = 120

1. Use FOIL (Distribute):

4x^2 + 20x +8x + 40 = 120

2. Group like terms:

4x^2 + 28x+ 40 = 120

3. Subtract 120 from both sides:

4x^2 + 28x - 80 = 0