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

Answer:

4x^2 + 28x - 80=0

Step-by-step 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

Answer 2

Answer:

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

Step-by-step 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,

$\text{Area}=\text{Length}\times \text{Breadth}$

Substitute the values,

$120=(2x+4)\times(2x+10)$

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

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

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

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

Therefore, option 3 is correct.