Question

Alexei wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.25 square feet. The mirror is 3 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?. . A. 2x2 + 8x - 19.25 = 0. B. 3x2 + 5x - 19.25 = 0. C. 4x2 + 16x - 4.25 = 0. D. 4x2 + 16x + 15 = 0

Answer 1

The answer is letter C. 4x2 + 16x - 4.25 = 0.

The area of the mirror and frame together is 19.25 square feet. You deduct that with the area of the mirror (3ft x 5ft = 15ft) and you have 4.25 square feet.

Answer 2

Let

x---------> the thickness of the frame in feet

At-------> Area of the mirror and the frame in square feet

we know that

`At=19.25ft^(2)` ------> equation
`1`

`At=(3+2x)*(5+2x)\\ At=3*5+3*2x+5*2x+2x*2x\\ At=15+6x+10x+4x^(2) \\ At=4x^(2) +16x+15`--------> equation
`2`

equate equation
`1` and equation
`2`

`19.25=4x^(2) +16x+15\\ 4x^(2) +16x+15-19.25=0\\ 4x^(2) +16x-4.25=0`

therefore

the answer is the option

`C. 4x2 + 16x - 4.25 = 0`