Question

Please answer ASAP (show work)!

The width of a mirror is 2 in. Less than its length. The area of the mirror is 168 in. sq. Find the dimensions of the mirror.

Answer 1

Answer: 14 inches by 12 inches

Work Shown:

x = length

x-2 = width

area = length*width

area = x(x-2)

x(x-2) = 168

x^2-2x = 168

x^2-2x-168 = 0

Plug a = 1, b = -2, c = -168 into the quadratic formula.

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-(-2)\pm√((-2)^2-4(1)(-168)))/(2(1))\\\\x = (2\pm√(676))/(2)\\\\x = (2\pm26)/(2)\\\\x = (2+26)/(2) \ \text{ or } \ x = (2-26)/(2)\\\\x = (28)/(2) \ \text{ or } \ x = (-24)/(2)\\\\x = 14 \ \text{ or } \ x = -12\\\\`

Ignore x = -12 since we cannot have a negative length.

The only practical solution is x = 14.

If x = 14, then x-2 = 14-2 = 12

The rectangular mirror is 14 inches by 12 inches

Check: area = length*width = 14*12 = 168

The answers are confirmed.