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

Answer:

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

Step-by-step 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 $4x^2+14x-3=0$.

Answer 2

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