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

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

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

Answer 2

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.