Question

Sarah wants to hang a mirror in her room. The mirror and frame must have an area of 15 square feet. The mirror is 3 feet wide and 4 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

Answer 1

4-y×3-v=x is an equation.
Hope it helps!

Answer 2

`4x^2+14x-3=0`

Explanation:

We have been given that the mirror is 3 feet wide and the thickness of the frame is x, so width of the frame would be
`x+x=2x`.

The width of mirror with frame would be
`2x+3`.

Similarly, the length of the frame would be
`x+x=2x` and the length of mirror with frame would be
`2x+4`.

We know that area of rectangle is width times length, so area of frame with mirror would be
`(2x+3)(2x+4)`.

We are told that The mirror and frame must have an area of 15 square feet, so we can equate our equation with 15 as:

`(2x+3)(2x+4)=15`

Upon simplifying our equation, we will get:

`4x^2+8x+6x+12=15`

`4x^2+14x+12=15`

`4x^2+14x+12-15=15-15`

`4x^2+14x-3=0`

Therefore, our required equation would be
`4x^2+14x-3=0`.